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Joep van der Zanden
Sand Transport Processes in the Surf and Swash Zones
SAND TRANSPORT PROCESSES
IN THE SURF AND SWASH ZONES
Joep van der Zanden
Promotion committee:
prof. dr. G.P.M.R. Dewulf University of Twente, chairman and secretaryprof. dr. S.J.M.H. Hulscher University of Twente, promotordr. ir. J.S. Ribberink University of Twente, co promotorprof. dr. T. O’Donoghue University of Aberdeenprof. dr. B.G. Ruessink Utrecht Universityprof. dr. ir. A.J.H.M. Reniers Delft University of Technologyprof. dr. R. Ranasinghe UNESCO IHE & University of Twentedr. ir. J.J. van der Werf Deltares & University of Twentedr. ir. C.M. Dohmen Janssen University of Twente
The work presented in this thesis was performed at the Department of WaterEngineering and Management, Faculty of Engineering Technology, of the University ofTwente. This research is supported by the Dutch Technology Foundation STW, which ispart of the Netherlands Organisation for Scientific Research (NWO) and partly fundedby the Ministry of Economic Affairs (project number 12058), with additional funding byEPSRC (EP/J00507X/1, EP/J005541/1) through the joint UK/Dutch SINBAD project.
ISBN: 978 90 365 4245 6DOI: 10.3990/1.9789036542456URL: http://dx.doi.org/10.3990/1.9789036542456Cover photo: Waves breaking on the Aberdeen beach (by Joep van der Zanden)Printed by Gildeprint Drukkerijen, Enschede, The Netherlands
Copyright © 2016 by Joep van der Zanden, Enschede, The Netherlands
All rights reserved. No part of this publication may be reproduced, stored in a retrievalsystem, or transmitted, in any form or by any means, without the written permission ofthe author.
SAND TRANSPORT PROCESSES
IN THE SURF AND SWASH ZONES
PROEFSCHRIFT
ter verkrijging van
de graad van doctor aan de Universiteit Twente,
op gezag van de rector magnificus,
prof. dr. T.T.M. Palstra,
volgens besluit van het College voor Promoties
in het openbaar te verdedigen
op vrijdag 9 december 2016 om 14.45 uur
door
Joep van der Zanden
geboren op 11 oktober 1987
te Roermond
Dit proefschrift is goedgekeurd door:
prof. dr. S.J.M.H. Hulscher promotor
dr. ir. J.S. Ribberink co promotor
A grain of sand is a moment of creation,
and the universe has taken millions of years to create it.
So all you have to do is contemplate a simple grain of sand,
and you will see in it all the marvels of the world.
Paulo Coelho (the Alchemist)
Contents
Contents
Preface.................................................................................................................................................. 11
Summary ............................................................................................................................................. 14
Samenvatting...................................................................................................................................... 17
1 Introduction................................................................................................................................ 20
1.1 Research context ................................................................................................................. 20
1.2 Cross shore hydrodynamic and sand transport processes........................................... 22
1.3 Practical sand transport models ....................................................................................... 27
1.4 Problem statement and research questions .................................................................... 29
1.5 Methodology ....................................................................................................................... 30
1.6 Outline ................................................................................................................................. 32
2 Near bed hydrodynamics and turbulence below a large scale plunging breaking waveover a mobile barred bed profile.................................................................................................... 34
2.1 Introduction......................................................................................................................... 36
2.2 Experiments......................................................................................................................... 37
2.2.1 Facility and test conditions ....................................................................................... 37
2.2.2 Instrumentation .......................................................................................................... 38
2.2.3 Measurement procedure ........................................................................................... 40
2.2.4 Morphology and experimental repeatability.......................................................... 42
2.2.5 Data treatment ............................................................................................................ 42
2.3 Water surface elevation and outer flow velocities ........................................................ 45
2.3.1 Surface elevation......................................................................................................... 45
2.3.2 Outer flow velocities .................................................................................................. 47
2.4 Near bed and wave bottom boundary layer (WBL) flow............................................. 48
2.4.1 Phase averaged velocities ......................................................................................... 48
2.4.2 Time averaged velocities........................................................................................... 50
2.4.3 Periodic velocities and wave bottom boundary layer thickness ......................... 51
2.5 Turbulence........................................................................................................................... 54
Contents
2.5.1 Time averaged turbulent kinetic energy................................................................. 54
2.5.2 Time varying turbulent kinetic energy ................................................................... 56
2.5.3 Reynolds shear stress ................................................................................................. 59
2.6 Discussion............................................................................................................................ 60
2.7 Conclusions ......................................................................................................................... 63
2.A. Additional information on ACVP measurements and data treatment........................... 64
3 Suspended sediment transport around a large scale laboratory breaker bar ................ 68
3.1 Introduction......................................................................................................................... 70
3.2 Experimental description .................................................................................................. 71
3.2.1 Facility and test conditions ....................................................................................... 71
3.2.2 Instrumentation .......................................................................................................... 73
3.2.3 Measurement procedure ........................................................................................... 75
3.2.4 Data treatment ............................................................................................................ 75
3.3 Bed evolution and hydrodynamics.................................................................................. 77
3.4 Suspended sediment transport processes....................................................................... 79
3.4.1 Suspended sediment concentrations ....................................................................... 80
3.4.2 Cross shore sediment flux......................................................................................... 84
3.4.3 Cross shore advection, pick up, and deposition.................................................... 90
3.5 Discussion............................................................................................................................ 96
3.6 Conclusions ......................................................................................................................... 98
4 Bedload and suspended load contributions to the morphodynamics of a large scalelaboratory breaker bar .................................................................................................................... 100
4.1 Introduction....................................................................................................................... 102
4.2 Experimental description ................................................................................................ 104
4.2.1 Facility and test conditions ..................................................................................... 104
4.2.2 Instrumentation ........................................................................................................ 104
4.2.3 Measurement procedure ......................................................................................... 107
4.2.4 Sediment characteristics .......................................................................................... 107
4.2.5 Data treatment .......................................................................................................... 108
4.3 Hydrodynamics and bed profile evolution .................................................................. 110
4.3.1 Hydrodynamics ........................................................................................................ 110
4.3.2 Bed profile evolution and net total transport ....................................................... 111
4.4 Bedload transport processes ........................................................................................... 113
4.4.1 Sheet flow layer concentrations.............................................................................. 113
Contents
4.4.2 Sheet flow layer thickness ....................................................................................... 115
4.4.3 Sheet flow particle velocities and fluxes ............................................................... 117
4.4.4 Net bedload transport rates .................................................................................... 119
4.5 Contributions of transport components to bar morphodynamics ............................ 122
4.5.1 Bedload and suspended load contributions to total transport .......................... 122
4.5.2 Bedload and suspended load transport contributions to bed profile change.. 124
4.6 Grain size sorting ............................................................................................................. 125
4.6.1 Vertical sorting of suspended sediment................................................................ 125
4.6.2 Cross shore sorting in the bed ................................................................................ 127
4.7 Discussion.......................................................................................................................... 128
4.8 Conclusions ....................................................................................................................... 130
5 Laboratory measurements of intra swash bed level and sheet flow behavior............ 132
5.1 Introduction....................................................................................................................... 134
5.2 Description of CCM+ ....................................................................................................... 136
5.2.1 Hardware................................................................................................................... 136
5.2.2 Signal processing and bed level tracking system................................................. 138
5.3 Description of the experiments....................................................................................... 139
5.3.1 Experimental set up ................................................................................................. 139
5.3.2 Wave conditions ....................................................................................................... 141
5.3.3 CCM+ settings............................................................................................................ 143
5.4 Morphological evolution of the swash zone................................................................. 143
5.5 Bed level motions in the lower swash ........................................................................... 146
5.5.1 Spectral analysis ....................................................................................................... 146
5.5.2 Bed level motions at time scale of the wave group sequence (TR = 195 s) ........ 147
5.5.3 Bed level motions during individual swash events ............................................ 149
5.6 Sheet flow dynamics ........................................................................................................ 152
5.6.1 Vertical concentration profiles................................................................................ 153
5.6.2 Time series of sheet flow concentrations............................................................... 155
5.6.3 Particle velocities and fluxes in the sheet flow layer........................................... 156
5.6.4 Sheet flow layer thickness ....................................................................................... 158
5.7 Discussion.......................................................................................................................... 158
5.7.1 Bed level motions at various time scales............................................................... 158
5.7.2 Sheet flow dynamics and implications for modeling sheet flow transport in theswash zone ................................................................................................................................ 160
Contents
5.8 Conclusions ....................................................................................................................... 161
5.A. Evaluation of CCM+ bed level measurements .................................................................. 162
5.A.1 Evaluation of CCM+ in the spectral domain ............................................................... 162
5.A.2 Evaluation of the CCM+ bed level tracking system in the time domain at short (intrawave group) time scales .......................................................................................................... 164
5.A.3 Discussion of CCM+ capabilities................................................................................... 164
6 Discussion................................................................................................................................. 166
6.1 Methodology ..................................................................................................................... 166
6.1.1 Experimental constraints......................................................................................... 166
6.1.2 Scale of experiments................................................................................................. 168
6.1.3 Wave conditions ....................................................................................................... 169
6.1.4 Instrumentation ........................................................................................................ 170
6.2 Implications for morphodynamic modeling ................................................................ 172
6.2.1 Wave averaged approach in morphodynamic models....................................... 172
6.2.2 Turbulence in breaking zone .................................................................................. 174
6.2.3 Suspended sediment transport in breaking zone ................................................ 174
6.2.4 Bedload transport in breaking zone....................................................................... 176
6.2.5 Sediment transport in the swash zone................................................................... 176
7 Conclusions and recommendations..................................................................................... 178
7.1 Conclusions ....................................................................................................................... 178
7.2 Recommendations ............................................................................................................ 181
References......................................................................................................................................... 184
About the author.............................................................................................................................. 200
Preface
11
Preface
Hoe interessant het gedrag van zandkorreltjes en waterdeeltjes ook is, deze studie wasonmogelijk zonder de inspiratie van de mensen om me heen. Iedereen die me geholpen heeft,hetzij door goede wetenschappelijke adviezen of juist door momentjes van ontspanning, wilik daarom van harte bedanken. Dit boekwerk is ook een beetje van jullie..!
Allereerst wil ik Jan ontzettend bedanken voor de intensieve begeleiding. Van begin tot eindbleek je een schier onuitputtelijke bron van kennis en ideeën, en je bevlogenheid bracht me ertelkens toe om nog even een extra onderzoeksstap te zetten. Bovendien voelde je haarfijn demomenten aan waarop het even wat minder lekker liep, en koos je ook op die momenten dejuiste toon.
Suzanne, dankzij de uitvoerige samenwerking met Jan en andere SINBAD collega’s volstondvoor jou een rol wat meer op de achtergrond. Juist daardoor kon je mijn schrijfsels als neutralelezer en met frisse blik beoordelen. Bedankt voor alle nuttige feedback, met name tijdens deeindfase.
Dominic, zonder jouw bijdrage was ik nog niet veel verder gekomen dan zand scheppen inhet lab. Zes maanden met jou opgescheept zitten in Barcelona was weliswaar vermoeiend (een9 tot 5 mentaliteit is jou vreemd) maar tegelijkertijd een gezellige en goede leerschool (aan bodkwamen de interessantste papers, de handigste Matlab routines, de beste recepten, deobscuurste hiphop, de lekkerste biertjes, en de flauwste Breaking Bad woordgrappen). Ookmijn ‘sabbatical’ halfjaar in Aberdeen was een groot succes, vooral dankzij de gastvrijheid vanjou en Bee – bedankt, en ik kom graag nog eens op bezoek!
Among the best things this PhD research brought me was meeting so many wise, helpful,friendly and passionate researchers. Iván and CIEM lab colleagues, thanks for your hospitalityand your sacrifices during the experiments, I’m looking forward to visiting you in Barcelonaagain. David, it was always a pleasure discussing results with you, I especially appreciate yourincredible patience when thoroughly explaining the complex world of acoustics. Tom, yourfeedback on the results and my writings and your keen eye for detail were invaluable; I alsowant to thank you for hosting me at the University of Aberdeen. José, your lessons aboutwaves, sediment transport, and data processing techniques during my first PhD years provedto be priceless during the remainder of my research.
Who says that meetings are dull? The SINBAD project meetings were always something tolook forward to and I’m very grateful to all other involved researchers (Ming Li, Justin Finn,
Preface
12
Jebbe van der Werf, Alan Davies, Wouter Kranenburg, Niels Jacobsen, Mahesa Bhawanin andPeter Thorne) and users (Henk Steetzel, Noel Beech, Dirk Jan Walstra, James Sutherland) fortheir useful feedback and discussions. Special thanks to Àngels: during the daily struggle youwere often the one supporting me with good advice and positive vibes. It’s an honor thatyou’re one my paranymphs during the defense!
Van een dagelijkse sleur is geen sprake wanneer je gezellige collega’s hebt..! Erik, dankzij jouwhartelijkheid vond ik snel m’n draai bij WEM en in Enschede. Bedankt voor alle gezelligheidtijdens etentjes, borrels, en tochtjes op de racefiets! Juancho, we started around the same time,how great is it that we will defend our PhD’s on the same day?! ‘Living’ in W 105 was greatfun, especially when sharing similar humor and music preference – I still celebrate theoccasional Kanye Friday! Your vision on politics and life in general really widened my ownviews, but you especially supported me by confronting me with my bad habits. Lianne, alsrasechte sfeermaker bracht je ontzettend veel gezelligheid in onze vakgroep, ons kantoor inhet bijzonder. Het was fijn om een partner in crime te hebben bij het organiseren vanDagHappen en borrels! Pieter, na de wekelijkse lunchruns keerde ik altijd weer met een frisen leeg hoofd terug – met name dankzij de discussies over sport, het nieuws, en de kommeren kwel van de universitair onderzoeker, een en ander opgediend met een continue stroomaan de allerbeste woordgrappen. Geert, ook jij was altijd te porren voor een sociale activiteit,ongeacht of het een lunch(run), een etentje, een spelletjesavond, of een lange fietstocht betrof– bedankt voor de gezelligheid!
Graag wil ik Anke, Joke, Brigitte en Monique bedanken voor al het regelwerk achter deschermen en voor de sociale cohesie binnen WEM! René, bedankt voor je onmisbare hulptijdens mijn eerste jaar, met name bij het testen van het nieuwe CCM+ systeem. Voor degezellige dagelijkse babbels in de koffiecorner en tijdens de lunch( wandelingen) wil ik Abebe,Anouk, Bart, Bas, Denie, Filipe, Joanne, Jolanthe, Juliette, Kathelijne, Kurt, Leonardo, Michiel,Nicholas, Olav, Rick, Ronald, Suleyman, Wenlong en alle anderen hartelijk bedanken! Abe,Bram, Mick, Roelof en Sjoerd: bedankt voor jullie bijdragen aan dit onderzoek, ik hebontzettend veel van jullie geleerd.
Je zou het bijna vergeten, maar gelukkig is er ook nog een leven naast academia. Ik ben vereerdmet zoveel vrienden die me bleven ondersteunen, ook als ik me in de verste uithoeken vanEuropa begaf. Dit schrijvende besef ik me: wel opvallend dat ik in een paar maanden Aberdeenen Barcelona evenzoveel visite heb ontvangen als in al die jaren Enschede…
Lau, een betere mental coach dan jij kon ik niet treffen: bij momenten van twijfel aan mezelfstond je altijd paraat om mijn zelfvertrouwen weer wat op te vijzelen. Supermooi dat je ookparanimf wil zijn, van Zummere en nie bang! GJ, je buitenlandse avontuurtjes zijn nu wel mooigenoeg geweest hoor – al die tijd moest ik maar weer andere concert en fietsbuddy’s zoeken!Maar zonder gekkigheid: supermooi dat we nog steeds contact hebben en ik kijk uit naar devolgende racefietsvakantie in de bergen. Ken, als levensgenieter pur sang liet je me vaak ziendat er belangrijker zaken dan werk zijn. Je rust en wijze adviezen waren van grote steun, en ik
Preface
13
kijk ernaar uit om weer vaker te kunnen fietsen nu we allebei een burgerlijk huisje inWageningen betrokken hebben!
Van de hele dag stil zitten is nog nooit iemand gelukkig geworden, dus daarom wil ik graagal mijn sportbuddy’s bedanken dat ze me naast m’n PhD activeerden. Allereerst wil ik Arend,Dennis, Evelien, Evi, Feike, Imke, Ivo, Kim, Lennart, Levinus, Lex, Marloes, Mischa, Nout,Uwi, Willemijn en alle andere oud Tartleten bedanken voor de vriendschap tijdens en naasthet hardlopen. Berry, Renske en Tim: de etentjes en weekendjes met oud Thymos zijn altijdvanouds gezellig..! Ook alle Kronauten bedankt voor de gezelligheid tijdens en naast detrainingen.
Despite the diminishing hope of a successful breakthrough with our punk band, I very muchenjoyed the rehearsals with the Swafflers/Kapsalöns. Juancho, Filipe, Mireia and Gérard: manythanks for the good fun!
De families van Buul en van der Zanden wil ik bedanken voor hun betrokkenheid en voor deouderwetse gezelligheid wanneer we elkaar zien. Bovenal dank aan mijn opa’s en oma’sHarry, Riet, Frans en Truus: jullie hebben me altijd geïnspireerd om hard te werken, met liefdevoor de natuur en de medemens. Helaas hebben jullie allemaal wel het begin, maar niet heteind van dit promotietraject mee mogen maken. Ook wil ik hier graag de familie van de Boer(Roelof, Sierdje, Geert en Annie) danken: met een hoofd vol met resultaten encomputerscriptjes zijn de weekendjes in Boijl perfect om weer helemaal tot rust te komen.
Pap en mam: ontzettend fijn dat jullie er altijd voor me zijn, voor wijze raad of gewoon vooreen ontspannen weekendje. Broertje: altijd gezellig om je te zien en om samen op te trekkenom nieuwe muziek te ontdekken.
Tot slot wil ik graag m’n meisje Anneke bedanken. Na al mijn midweekjes Enschede, maandjesBarcelona en het halfjaartje Aberdeen, zijn we nog steeds niet van elkaar af..! Gelukkig maar,want jij weet vaak beter dan ikzelf wat me gelukkig maakt. Zonder jouw positieve energie, jelieve zorgzaamheid, en je geduld bij het aanhoren van mijn monologen over turbulentie, wasik nu vast al helemaal doorgedraaid. Ik kijk uit naar nieuwe avonturen saampjes!
Joep van der Zanden, November 2016
Summary
14
Summary
Coastal regions are in many ways relevant to society, but are widely threatened by erosion.Long term predictions of beach morphology using numerical models can help coastalmanagers to develop cost effective coastal protection strategies. Such models operate at a largespatial and temporal domain and rely on semi empirical parameterizations to account forunderlying small scale processes. Parameterizations for sand transport have mainly beendeveloped on the basis of measurements under non breaking waves. When these sandtransport models are applied to the wave breaking region and the swash zone – where wavesrun up and down on the beach – they fail at properly predicting sand transport rates. This isattributed to a lack of understanding of how sand transport is affected by additional breakingrelated processes.
The aim of this thesis is therefore to improve understanding of sand transport physics in thebreaking and swash zone. This objective is pursued through controlled experiments in a largescale wave flume with a mobile medium sand bed during two campaigns: one focusing on thebreaking region, the other on the swash zone. During both campaigns, the use of novelinstruments enables measurements of sediment transport processes near the bed with muchhigher resolution than during previous studies. Effects of wave breaking and flow nonuniformity on sediment transport dynamics are identified by comparing results with existingknowledge of sand transport dynamics for non breaking waves. The results are then used tosuggest improvements for sand transport models in the breaking and swash zone.
Chapters 2 to 4 present measurements of hydrodynamics and sand transport dynamics undera monochromatic plunging breaking wave around an evolving breaker bar. Chapter 2 focuseson the hydrodynamics in the breaking region, with particular interest on flow and turbulenceover the near bed region which includes the wave bottom boundary layer. The measurementsin this region, obtained with a prototype acoustic concentration and velocity profiler (ACVP),are believed to be the first measurements of the complete wave bottom boundary layer underlarge scale breaking waves. Wave breaking leads to large turbulence production and anincrease in turbulent kinetic energy (TKE) in the complete water column. Breaking generatedturbulence also invades the boundary layer. Near the plunge point, this invasion occurs duringtwo instances of the wave cycle: a first occurrence rapidly after wave plunging, and a secondoccurrence during the wave trough phase when undertow and periodic velocities transportTKE towards the breaker bar. The invasion results in an increase in TKE inside the wavebottom boundary layer with a factor 3 from shoaling to breaking region. Breaking generatedturbulence travels back and forth between breaking and shoaling region due to advection byorbital and undertow velocities. Consequently, the near bed region affected by wave breakingextends horizontally to about 3 m offshore from the plunge point. Time averaged velocities in
Summary
15
the wave bottom boundary layer are offshore directed and are generally dominated by theundertow. The non dimensional wave bottom boundary layer thickness increases with a factor2 3 in the breaking region, which is caused by flow divergence induced by the bar geometryand/or by effects of breaking generated turbulence.
Measurements during the same experiment are used in Chapter 3 to assess wave breakingeffects on suspended sediment transport processes and to examine the spatial distribution ofsediment fluxes. Sediment concentrations are measured at outer flow elevations using atransverse suction system and near the bed using the ACVP. The ACVP also measuresvelocities and allows the examination of collocated TKE and suspended sedimentconcentrations and fluxes in the near bed region with much higher resolution than previousstudies. Results show that suspended sediment concentrations increase by up to one order ofmagnitude from shoaling to breaking region. This is due to effects of breaking generatedturbulence, which does not only enhance vertical mixing but is in the present study alsoidentified as the main driver for sediment pick up. Outer flow wave averaged sediment fluxesare offshore directed over most of the water column, but significant onshore contributions arefound at elevations between wave trough and wave crest level in the breaking region and atelevations inside the wave bottom boundary layer at locations offshore from the plunge point.The latter is due to a significant onshore directed wave related suspended sediment transportcontribution that is generally confined to the wave bottom boundary layer. The measurementsare used to relate the spatiotemporal variation in suspended sediment concentrations tohorizontal advection and to vertical exchange between the bedload and suspension layer. Thisanalysis reveals that the entrainment of sediment in the bar trough occurs primarily duringthe wave trough phase, when both near bed velocity magnitude and near bed (breakinggenerated) TKE are highest. The entrained particles are almost instantly advected offshoreduring the wave trough phase, and are deposited near the bar crest during the wave crestphase when velocity magnitudes reduce. The suspended particles further follow an intra waveonshore offshore excursion between shoaling and breaking region. This excursion is consistentwith spatiotemporal patterns in TKE, which suggests that sediment particles are trapped inbreaking generated vortices that are advected back and forth following the orbital motion.
Chapter 4 focuses on effects of wave breaking on bedload and grain size sorting processes,and on bedload and suspended transport contributions to the breaker bar morphodynamics.Two novel conductivity based concentration measurement (CCM+) tanks measuredconcentrations and particle velocities in the bedload (sheet flow) layer at the breaker bar crest.Sheet flow layer concentrations and thicknesses do not reveal a significant effect of breakinggenerated turbulence, but are affected by cross shore advection of sediment. This shows thatbedload dynamics are not fully controlled by local hydrodynamic forcing. Net bedloadtransport rates show strong cross shore variation which relates firstly to variations inacceleration and velocity skewness (for locations from shoaling zone up to bar crest), andsecondly to variations in local bed slope and near bed TKE (in breaking region alongshoreward facing bar slope). During the experiment the bar slowly migrates onshore whilstits crest grows and its trough deepens. This occurs under the influence of (i) onshore directedbedload transport, which erodes the offshore bar slope and accretes the bar crest, and (ii)offshore directed suspended load, which induces net pick up at the bar trough and netdeposition at the bar crest. Both transport components are of similar magnitude, but bedload
Summary
16
dominates in the shoaling zone while suspended load is larger in the breaking and inner surfzone. Grain size distributions of suspended sediment samples show that sediment pick upand vertical mixing is size selective (i.e. the fraction of fine sediment is relatively large) in theinner surf zone in presence of vortex ripples, but size indifferent (i.e. also coarsest grains areentrained) in the breaking region in presence of large and energetic breaking inducedturbulent vortices. Selective transport by both bedload and suspended sediment transportleads to a cross shore coarsening of sediment in the bed from shoaling to inner surf zone.
Sediment transport in the swash zone is studied through another experimental campaign(Chapter 5). The novel CCM+ is deployed for the first time, and is used to study the responseof the sheet flow layer and the intra swash bed level to energetic swash events with strongwave swash interactions. The highly non uniform flow conditions under these swash eventslead to intra swash bed level changes of up to 1 cm, with rapid erosion during the early uprushphase and gradual accretion during the backwash. The bed level changes are explained bycross shore advection of sediment between the lower and mid/upper swash zone at an intraswash time scale. This advection also affects sheet flow concentrations and thicknesses,leading to much larger sheet flow thicknesses than expected based purely on the horizontaloscillatory velocities. Moreover, the sheet flow thickness increases temporally under events ofstrong wave backwash interactions that enhance local turbulence. Both factors (sedimentadvection and bore turbulence) may affect sheet flow transport rates in the swash zone.
The general discussion (Chapter 6) reflects on the implications of the present study’s resultsfor the future development of engineering type sand transport and morphodynamic models.
Summary
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Samenvatting
Kustgebieden zijn van groot maatschappelijk en economisch belang maar worden wereldwijdbedreigd door erosie. Langetermijnvoorspellingen van kustmorfologie met numeriekemodellen kunnen kustbeheerders helpen met het ontwikkelen van kosteneffectievekustbeschermingsstrategieën. Zulke modellen werken op een grote ruimte en tijdsschaal enberusten op eenvoudige formules van onderliggende fysische processen. Formules voorzandtransport zijn ontwikkeld op basis van metingen onder niet brekende golven. In hetgebied waar golven breken (branding) en het strand oplopen (golfoploopzone) hebben dezezandtransport formules echter een grote foutmarge. Hierdoor lukt het niet goed lukt om dekustdynamiek te modelleren. Deze foutieve voorspellingen komen voort uit een onvoldoendebegrip van zandtransportprocessen onder brekende golven.
Het doel van dit promotieonderzoek is daarom om de fysische processen van zandtransportin de branding en de golfoploopzone beter te begrijpen. Hiertoe zijn gecontroleerdeexperimenten met een mobiel zandbed in een grootschalige golfgoot gedaan. Resultaten vantwee meetcampagnes worden gepresenteerd: de eerste gericht op de branding, de tweede opde golfoploopzone. Tijdens beide campagnes zijn nieuwe meetinstrumenten ingezet diesedimenttransportprocessen aan het bed met veel hogere resolutie kunnen meten dan tijdensvoorgaande studies. De metingen worden vergeleken met eerdere observaties onder nietbrekende golven om zodoende de effecten van golfbreking en de niet uniformiteit van destroming op zandtransport te kunnen begrijpen. De resultaten worden vervolgens gebruiktom aanbevelingen te doen voor het verbeteren van zandtransportformules.
Hoofdstukken 2 tot 4 presenteren metingen van hydrodynamica en zandtransportprocessenrond een evoluerende brekerbank onder een regelmatige duikend (‘plunging’) brekende golf.Hoofdstuk 2 richt zich op de gemeten hydrodynamica, met name op de stroming enturbulentie nabij het bed, inclusief de golfbodemgrenslaag, waar een groot deel van hetsedimenttransport plaatsvindt. De metingen in deze laag, verkregen met een prototypeakoestische sensor voor concentratie en snelheidsprofielen (ACVP), zijn vermoedelijk deeerste metingen van de volledige golfbodemgrenslaag onder grootschalige brekende golven.Golfbreking leidt tot sterke productie van turbulentie en een toename in turbulente kinetischeenergie (TKE) over de gehele waterkolom. Deze turbulentie bereikt het bed, hetgeen tot eenfactor 3 toename van TKE in de grenslaag leidt in vergelijking met de pre breekzone. Deaankomst van turbulentie bij het bed gebeurt met name tijdens de golftrogfase, maarplaatselijk in de buurt van het breekpunt gebeurt dit ook tijdens de golftopfase. De brekinggeproduceerde turbulentie volgt de orbitaalsnelheden en reist zodoende op en neer tussen depre breekzone en de branding. De tijdsgemiddelde snelheden in de grenslaag wordengedomineerd door de retourstroom. De dimensieloze golfgrenslaagdikte neemt met een factor
Summary
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2 à 3 toe onder de brekende golf, wat verklaard kan worden door de toename in turbulentieen/of door stromingsdivergentie langs de steile helling aan de kustzijde van de brekerbank.
De effecten van golfbreking op gesuspendeerd sediment (concentraties en fluxen) in debrandingszone worden onderzocht in Hoofdstuk 3. Zandconcentraties zijn gemeten nabij hetbed (met de ACVP) en boven de golfbodemgrenslaag (met een afzuigsysteem). De ACVP meetook snelheden en levert simultane metingen van TKE en suspensieconcentraties en –fluxenmet veel hogere resolutie dan voorgaande studies. Resultaten laten zien dat zandconcentratiesmet een orde grootte toenemen van de pre breekzone naar de branding. Dit komt door debreking geproduceerde turbulentie, die in deze studie niet alleen zorgt voor sterkere verticalemenging maar ook voor het oppikken van sediment aan het bed. Suspensiefluxen zijnzeewaarts gericht over het gros van de waterkolom, maar significante kustwaartse fluxen zijngemeten boven golftrogniveau in de branding en in de golfbodemgrenslaag in de metingenvoor het breekpunt. Deze laatste kustwaartse fluxen worden verklaard door een significantebijdrage van het golfgerelateerde suspensietransport dat over het algemeen beperkt blijft totde golfbodemgrenslaag. De resultaten laten verder een complex patroon van intra golfsedimentconcentratieveranderingen zien. Deze veranderingen komen door horizontaleconvectie en door verticale uitwisseling van sediment tussen de bodemtransportlaag en desuspensielaag. Zeewaarts van de top van de brekerbank reist het sediment horizontaal op enneer op eenzelfde manier als de brekinggeproduceerde turbulentie. In het gebied tussen detop en trog van de brekerbank worden sedimentconcentratieveranderingen verklaard dooropwerveling (boven de trog van de bank), zeewaartse afvoer, en depositie (op de top van debank), waarbij elke term sterk verandert binnen de golfcyclus.
Hoofdstuk 4 behandelt de effecten van golfbreking op bodemtransportprocessen enkorrelgroottesortering, en behandelt verder hoe het bodem en suspensietransport bijdraagtaan de groei van de brekerbank. Zandconcentraties en korrelsnelheden in debodemtransportlaag (sheetflowlaag) zijn gemeten op de brekerbank met twee nieuwgebouwde geleidbaarheidstype meetsystemen (CCM+). Concentraties en diktes van desheetflowlaag laten geen effecten zien van de aanwezige externe turbulentie, maar wordenwel beïnvloed door horizontaal aangevoerd sediment. Het netto bodemtransport verandertduidelijk langs de brekerbank. Deze variatie wordt met name bepaald door veranderingen inde golfvorm en in de lokale helling en aanwezige TKE. Tijdens het experiment migreert debrekerbank richting de kust terwijl de banktop groeit en de zandtrog zich verdiept. Dit komtdoor een combinatie van (i) kustwaarts gericht bodemtransport, dat leidt tot erosie van dezeewaartse helling en depositie op de top van de bank, en (ii) zeewaarts gerichtsuspensietransport, dat leidt tot erosie van de zandtrog en depositie op de bank. Beidetransportcomponenten zijn van vergelijkbare grootte, maar bodemtransport domineert voorhet breekpunt en suspensietransport na het breekpunt. Korrelgrootteverdelingen vansuspensiemonsters laten zien dat de grote turbulente wervels in de breekzone weinigonderscheid maken tussen korrels van verschillende grootte, terwijl de kleinere wervels opandere locaties zorgen voor een verticale differentiatie in korrelgrootteverdeling vangesuspendeerd sediment (i.e. het gesuspendeerde sediment is relatief fijner). Door selectiefbodem en suspensietransport wordt de korrelgrootte in het bed steeds fijner in de prebreekzone en steeds grover in de branding.
Summary
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Het zandtransport in de golfoploopzone is bestudeerd tijdens een ander experiment(Hoofdstuk 5). De CCM+ is tijdens dit experiment voor het eerst toegepast, en wordt gebruiktom de reactie van de sheetflowlaag en het bedniveau op een energieke golfoploop met sterkegolf golfoploop interacties te bestuderen. Doordat het stromingsveld onder de energiekegofoploopcondities sterk niet uniform is, verandert het bedniveau sterk (fluctuaties à 1 cm)binnen de golfoploopcyclus. Tijdens de eerste fase van de golfoploop, wanneer golvenomhoog lopen op het strand, treedt een plotse, sterke erosie van het bed op. Tijdens de tweedefase van de golfoploop, wanneer het water vanaf het strand terugstroomt, keert het bedlangzaam terug naar vrijwel het originele niveau. Dit wordt verklaard door een horizontaleexcursie van sediment tussen verschillende gebieden binnen de golfoploopzone. Dezeexcursie beïnvloedt ook de sheetflowlaag: deze is veel dikker dan verwacht op basis van enkelde horizontale oscillerende snelheid. De sheetflowlaag wordt bovendien sterk beïnvloed doorturbulentie opgewekt door de interacties tussen verschillende golven. Deze turbulentie en dehorizontale advectie van sediment hebben mogelijk een sterke invloed op het bodemtransportin de golfoploopzone.
De discussie in Hoofdstuk 6 spitst zich onder meer toe op hoe de nieuw verkregen inzichtenkunnen bijdragen aan het verbeteren van zandtransportformules en morfodynamischemodellen.
Chapter 1
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1 Introduction
1.1 Research context
Coastal regions are often densely populated and offer various services to society. In theNetherlands, the primary function of the coast is the protection of the hinterland againstflooding. Other functions of coastal zones include industries and harbors, drinking watersupply, tourism, aquaculture, and ecology (Giardino et al., 2011). At the same time, coasts aredynamic areas. At sandy shores (Figure 1.1), sediment is continuously transported in crossshore and alongshore direction under action of tides, wind waves, and (wave induced)currents. During calm weather conditions, cross shore sediment transport is generallydirected shoreward, leading to accretion of the shoreface. Aeolian processes lead to furtherinland directed transport of sediment grains and promote dune growth. However, duringstorms, energetic waves entrain large amounts of sediment that are transported offshore bywave induced currents, hence resulting in net erosion of the beach.
The erosion rate of coasts increases as a result of sea level rise, land subsidence, and increasedstorminess (Giardino et al., 2011) and threatens coasts around the world. Human interferences,such as damming of rivers and estuaries, the application of hard structures for coastalreinforcement, and sand and gas mining, may alter the sediment budget and enhance (local)coastal erosion (Giardino et al., 2011; Van der Spek and Lodder, 2015). Averaged over thecomplete Dutch coastline, these processes lead to a structural net erosion of the shoreface,beach and frontal dunes areas of an estimated 2.6 million m3 per year over the period 19902005 (Van der Spek and Lodder, 2015). Such erosion forms a direct threat to services providedby the coastal region – safety of the inland not being the least of them.
Current Dutch policy in coastal management is directed at maintaining the coastline of 1990,plus creating an extra buffer to cope with future threats (Giardino et al., 2011). This is typicallyachieved through sand nourishments (7.4 million m3/y between 1990–2005), that are preferablyapplied to the shoreface and not directly to the beach in order not to disrupt beach functionsand to save costs (Van der Spek and Lodder, 2015). Once in place, the nourished sand isgradually transported onshore under action of the short wind waves, but also acts as a barrierthat forces the most energetic waves to break – hence reducing wave energy and erosion ratesat the shoreline (Van Duin et al., 2004).
Coastal management can benefit from medium (5 years) and long term predictions of coastalmorphology that support understanding of the natural behavior of coastal regions. Suchpredictions can be made using morphodynamic numerical models (Delft3D, Mike, TELEMAC,XBeach) that couple equations for hydrodynamics (waves and currents), sediment transport(bedload and suspension) and bed level changes. Such morphodynamic models operate on alarge spatiotemporal domain and rely on parameterizations of small scale underlying
Introduction
21
processes. Sand transport rates are calculated using semi empirical formulations, discussed inmore detail in Section 1.3. These sand transport models are largely based on observations ofsand transport processes and transport rates in controlled laboratory conditions, i.e. inoscillatory flow tunnels or wave flumes with non breaking waves (Van Rijn et al., 2013), andthey generally do not consider effects of wave breaking.
Figure 1.1. Waves approaching the beach in Southern Australia. Photo by Carel van der Zanden
Simulations with morphodynamic models can also be used to assess the (cost )effectiveness ofdifferent management (nourishment) strategies, hence supporting decision making andcontributing to cost reduction. This requires a good model performance in terms of simulatinghydrodynamics and cross shore sediment transport processes in the near shore region. Theperformance of morphodynamic models in terms of simulating cross shore sand bar migrationwas assessed in a number of studies by Van Rijn et al. (2003; 2007d; 2011). It was shown thatbar migration for erosive laboratory conditions can be simulated ‘reasonably well inqualitative sense’ (Van Rijn et al., 2007d; 2011), although results do show a mismatch betweenthe exact location and shape of the migrated bar near the location of wave breaking. ‘Bad’results were obtained when simulating accretive conditions (Van Rijn et al., 2011), mainly dueto over prediction of erosion rates near the shoreline.
It is concluded that sediment transport in the inner surf and swash zone cannot be properlypredicted, which is partly explained by the swash erosion method (Section 1.3) being too crude(Van Rijn et al., 2011). In addition, net transport in this region is the (relatively small) residualof (much larger) offshore and onshore directed transport components, and is thereforenotoriously difficult to predict (Van Rijn et al., 2003; 2007d). Not surprisingly, the discrepanciesbetween modelled and measured sand bar evolution grow when the time scale is increased toseasonal scale (Van Rijn et al., 2003). These results show a direct need of improving sandtransport model formulations for the near shore (breaking to swash zone) region. To advancetransport models, it is essential to first improve understanding of hydrodynamic and sedimenttransport processes in the breaking and swash zone.
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1.2 Cross shore hydrodynamic and sand transport processes
This study focuses on cross shore sand transport processes in the near shore region from thewave breaking point up to the swash zone. Figure 1.2 illustrates the coexistence of differentsediment transport mechanisms along a cross shore barred profile, and serves as a referencefor the applied terminology. The present section offers a concise description of near shoresediment transport processes and identifies scientific knowledge gaps that are assessed in thisthesis.
Wave dynamics
When waves approach the shore, their wave height increases as their celerity decreases.During this shoaling process, waves become increasingly non linear due to energy transferfrom the primary wave components to their higher harmonics (Phillips, 1960; Elgar and Guza,1985). This results in skewed waves that are horizontally asymmetric, i.e. with high shortduration crests and long duration flat troughs. The higher harmonic constituents partially actas ‘free’ superimposed waves (Phillips, 1960) that lag the primary wave (Flick et al., 1981; Bejiand Battjes, 1993). This leads to asymmetric (saw tooth shaped) waves, in which the term‘asymmetric’ now refers to asymmetry in the vertical plane.
Figure 1.2. Conceptual drawing of cross shore sediment processes in the near shore region.
With increasing asymmetry, also the steepness of the wave front increases, eventually leadingto wave breaking. This can happen in different ways (plunging, spilling, surging, collapsing),depending on wave and bed profile characteristics (Battjes, 1974). Wave breaking leads to areduction in wave energy and in wave height. The breaking front develops into a surf bore (alsocalled surface roller) which continues propagating shoreward along the inner surf zone (regionbetween breaking point and the shoreline) while dissipating wave energy. Upon reaching theshore, the surf bore runs up on the beach while decelerating due to friction and gravitationalforces. The fluid that has ran up on the beach then retreats and accelerates in offshore directionduring the backwash phase. The region of beach run up/run down is termed the swash zone.Important for further discussions in this thesis is that hydrodynamics in the swash zone arenot solely determined by individual incident short waves, but also by energy contained inwave groups (Baldock et al., 2000). In addition, wave swash interactions importantly affect
Shoaling zone: wave height grows,increasing steepness of wave front
Sea
Breaking zone: wave energy dissipation,production of turbulent vortices
Inner surf zone: highlyaerated and turbulent bore
Swash zone: Run up andrun down of waves/bores
Orbital velocity motion
Turbulent vortices
Vortex ripples
Suspended particles
Suspendedparticles Undertow
profile
Breaker trough
Breakerbar
Beach
Introduction
23
hydrodynamics (run up, velocities) and sediment transport processes (e.g. Hughes andMoseley, 2007; Caceres and Alsina, 2012).
Time averaged velocities
Velocities can be split in a time averaged (net current), orbital, and turbulent component. Furtherdistinction is made between the wave bottom boundary layer (the near bed region at whichorbital velocities are affected by presence of the bed) and the outer flow (above the wave bottomboundary layer, up to wave crest level).
Outer flow net currents are generally offshore directed in the lower half of the water columnas they compensate for the onshore mass flux (Stokes drift) that occurs especially above wavetrough level. This time averaged return current is termed undertow. In breaking/broken waves,the onshore mass flux contained in the roller is larger than the mass flux associated with theStokes drift for non breaking waves (Svendsen, 1984). Furthermore, the reduction in waveheight results in a horizontal momentum flux gradient that drives a horizontally positive(towards the beach) time averaged pressure gradient (set up/set down) (Stive and Wind,1986). The combination of mass flux increase and the positive pressure gradient leads to anincrease in offshore directed undertow velocities in the breaking region. The shape of theundertow profile is defined by the depth varying momentum equations which include, nextto horizontal gradients in momentum and pressure, terms related to vertical exchange ofhorizontal momentum by orbital and turbulent velocities (e.g. Svendsen, 1984). All thesecontributions exhibit strong cross shore variation, and consequently, time averaged flow inthe breaking region is strongly non uniform in cross shore direction.
Orbital velocities have an oscillatory nature, i.e. vary in magnitude and direction during thewave cycle. At outer flow elevations, orbital velocities are in phase with the water surface leveland are directed onshore below the wave crest and offshore below the wave trough. Thecontinuous flow acceleration and deceleration is caused by the time varying horizontalpressure gradient under progressing waves. Under skewed waves, the orbital crest velocitiesexceed those during the trough. For asymmetric waves, the acceleration during the zero upcrossing (flow reversal from trough to crest) exceeds the acceleration during the zero downcrossing of the wave. Both these processes (termed orbital velocity skewness and asymmetry) leadto a higher bed shear stress exerted by the orbital motion during the crest phase than during thetrough phase.
Orbital velocity magnitudes decrease rapidly in a small (compared to the full water column)layer close to the bed. Inside this wave bottom boundary layer, horizontal pressure gradients arenot the only forcing term for local fluid acceleration/deceleration. Instead, velocities areretarded by bed friction forces that act in the direction opposing the instantaneous velocityvector. The combined forcing of horizontal pressure gradient and bed friction factors yields aphase lead of orbital velocities inside the wave boundary layer over the velocities at free streamelevations in the outer flow directly above this layer. The wave bottom boundary layer isfurther characterized by time averaged cross shore velocities that relate to streamingmechanisms, i.e. onshore progressive wave streaming under surface waves because horizontaland vertical orbital velocities are not exactly 90° out of phase, and offshorewave shape streaming
Chapter 1
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under skewed and asymmetric waves due to differences in bed generated turbulenceintensities between the crest and trough half cycle (discussed extensively by Kranenburg,2013).
The effects of wave breaking on boundary layer hydrodynamics have not yet been examinedin detail. Instead, most previous detailed observations of the wave bottom boundary layerwere obtained in oscillatory tunnels (e.g. Jonsson and Carlsen, 1976; Sleath, 1987; Jensen et al.,1989; van der A et al., 2011) or under non breaking waves (Conley and Inman, 1992; Foster etal., 2000; Foster et al., 2006a; Schretlen, 2012). An oscillatory flow tunnel experiment with gridinduced turbulence did show that external (breaking generated) turbulence importantlyaffects time averaged velocities and turbulence dynamics inside the wave bottom boundarylayer (Fredsoe et al., 2003).
Turbulence
Turbulent velocity fluctuations are irregular fluctuations associated to 3 dimensional vortices(or: eddies) and can be generated by a moving fluid’s internal shear or by friction with anexternal object (e.g. Pope, 2000). In the present breaking wave study, bed friction and wavebreaking/surf bores are the primary turbulence production sources (e.g. Feddersen et al., 2007).The magnitude of turbulent fluctuations is commonly expressed in terms of turbulent kineticenergy. The turbulent kinetic energy is not fully locally determined, since turbulence spreadshorizontally and vertically through advection and diffusion processes (Ting and Kirby, 1995;Boers, 2005). Turbulent vortices are unstable and step wise break up into smaller vortices, aprocess that continues until viscous shear stresses trigger the conversion of smallest eddiesinto heat (turbulence dissipation).
Based on turbulence observations in small scale wave flumes, it has been hypothesized thatthe correlation between time varying breaking generated turbulent kinetic energy and wavephase may contribute to onshore or offshore directed sediment transport (Ting and Kirby,1995; Boers, 2005; De Serio and Mossa, 2006). However, the intra wave variation in breakinggenerated turbulence at the bed has never been examined for large scale conditions. Instead,most previous studies under large scale breaking waves in field (e.g. Ruessink, 2010; Grassoet al., 2012) and laboratory (e.g. Scott et al., 2005; Yoon and Cox, 2010) focused on time averagedturbulence quantities at outer flow elevations. Therefore, it remains unclear how breakinggenerated turbulence may affect time varying turbulent kinetic energy near the bed, inside thewave bottom boundary layer, and how this in return affects sediment transport.
Bedload transport processes
Total sediment transport in the near shore region is partitioned into: (i) a bedload component,which may be defined on physical arguments as the fraction of sediment grains that issupported by intergranular forces (Bagnold, 1956; Nielsen, 1992) or, more practically, as themoving sediment grains below a particular reference elevation close to the bed (e.g. Van Rijn,2007a); (ii) a suspended load component, primarily driven by turbulence induced fluid drag(Bagnold, 1956; Nielsen, 1992) and found above the near bed reference level (Van Rijn, 2007b).
Introduction
25
Suspended sediment fluxes can be split into a current related (product of wave averagedvelocities and time averaged concentrations) and a wave related (product of oscillatory/demeaned velocities and concentrations) component. The latter can be non zero in case sedimentconcentrations are time dependent during the wave cycle, i.e. in occurrence of higher sedimentconcentrations during one of the wave half cycles (crest and trough phase) relative to theother.
Figure 1.3. Snapshots of sheet flow transport in a small scale oscillating flow tunnel with fine sand. (a)Start of flow cycle with bed at rest; (b) At maximum orbital velocity, showing a well developed sheet
flow layer with high sediment concentrations; (c) Around flow reversal, showing break up of thesheet flow layer and the formation of suspension events. Snapshots are taken from video recordings
by the author during experiments at the University of Twente as part of the CCM+ development(Chapter 5).
For mildly energetic conditions (e.g. inner surf zone and at deeper water more offshore), bedforms such as vortex ripples generally appear. Characteristic for these conditions is the ejectionof sediment laden vortices around each flow reversal (twice per wave cycle), which aretransported during the subsequent half cycle (Van der Werf et al., 2007).
In the breaking region and the swash zone, the energetic waves/surf bores and relativelyshallow water depths result in large velocity magnitudes near the bed. If peak velocities aresufficiently large, bed forms are faded out and sediment grains are transported in a thin(O(mm)) high concentration (100 – 1600 g/L) layer that grows and decays during a wave cycle(Horikawa et al., 1982; Ribberink and Al Salem, 1995). Figure 1.3 shows visual observations ofsuch sheet flow transport. For medium sand, sand transport in the sheet flow layer respondsquasi instantaneously to bed shear exerted by the flow (Ribberink and Al Salem, 1995;O Donoghue and Wright, 2004a). Consequently, under skewed/asymmetric waves, the higherpeak bed shear stresses during the crest (relative to trough) phase result in onshore directedbedload transport for medium sand (O Donoghue and Wright, 2004b; Schretlen, 2012). Undernon breaking waves, where suspended sediment concentrations are low, the majority ofdepth integrated transport over the complete water column is confined to the sheet flow layer(Dohmen Janssen and Hanes, 2005; Schretlen, 2012).
Transport rates in the sheet flow layer are large and can form a major contribution to totaltransport rates and to near shore morphology. Sheet flow dynamics have predominantly beenstudied in oscillating flow tunnels or in wave flumes with uniform non breaking waves. Animportant question from scientific and engineering perspective is whether wave breaking, e.g.due to penetration of breaking generated turbulence into the wave bottom boundary layer,can significantly affect bedload (sheet flow) transport rates. Observations of bedload transportin a steady flow tunnel with grid induced turbulence revealed that the presence of externalturbulence can significantly enhance bedload transport rates (Sumer et al., 2003). However, no
Chapter 1
26
measurements have been able to reveal if breaking generated turbulence can affect bedloadtransport rates and processes.
Suspended sediment transport processes
The bed shear may also lift sediment grains from the bed and bring them into suspension. Thislift is driven by an upward directed pressure gradient that is associated with bed shearinduced ejected vortices (Sumer and Oguz, 1978). Once suspended, gravitational settling andvertical advective and diffusive mixing lead to vertical concentration profiles that follow anexponential or power function distribution, depending on the vertical distribution ofturbulent kinetic energy (Aagaard and Jensen, 2013). Under breaking waves, higherentrainment and mixing rates lead to an increase in concentrations at outer flow elevationscompared to shoaling locations (Nielsen, 1984; Nadaoka et al., 1988; Aagaard and Jensen, 2013).The increased pick up rates under breaking waves can be attributed to high instantaneous bedshear stresses (Cox et al., 1996) and to upward directed pressure gradients in the bed underthe breaking point (Sumer et al., 2013).
The current related transport is the depth integrated product of time averaged concentrationsand velocities (undertow plus streaming profile). Depending on vertical distributions of bothvariables, the current related transport can be directed offshore or onshore for non breakingwaves. The net current related transport is generally directed offshore in the breaking region,due to the increase in undertow magnitudes and in suspended sediment load at outer flowelevations. If net suspended transport rates are non uniform, as expected in the breakingregion, sediment concentrations at a particular cross shore location are not only controlled bylocal vertical processes (i.e. pick up/deposition and vertical mixing plus settling) but also bythe net influx of suspended sediment from adjacent locations (Hanes and Huntley, 1986). Thisis notably different from suspended transport under non breaking (shoaling) waves overhorizontal beds, which is cross shore uniform at a wave averaged time scale.
Based on experimental observations of time varying turbulence, several small scale studieshave suggested an enhanced wave related suspended transport rate under plunging waves(Ting and Kirby, 1995; Boers, 2005; De Serio and Mossa, 2006). Onshore directed wave relatedsuspended fluxes have indeed been observed in the breaking region (Ruessink et al., 1998;Aagaard and Hughes, 2010; Yoon and Cox, 2012). However, it is not evident whether thisrelates to breaking induced turbulent kinetic energy or to wave asymmetry; both parametersare interrelated (as pointed out by van Thiel de Vries et al., 2008). Collocated measurements ofturbulence and suspended sediment concentrations in the near bed region, which includes thewave bottom boundary layer, may likely contribute to the understanding of breakinggenerated turbulence effects on wave related suspended sediment transport.
Sediment transport in the swash zone
The swash zone is characterized by high instantaneous sediment fluxes in both onshore(during uprush) and offshore (backwash) direction, and a relatively small residual net (swashevent averaged) transport rate (Masselink and Puleo, 2006). High fluxes of bedload (sheet
Introduction
27
flow) and suspended load are particularly found during the early uprush and late backwashphases, when velocity magnitudes are at maximum. High suspended sediment concentrationsduring the uprush phase relate to large amounts of sediment entrained locally by the highlyturbulent flow under surf bores (Puleo et al., 2000) but also to pre suspended sediment whichis advected from the inner surf zone into the swash zone (Jackson et al., 2004). Wave swashinteractions may lead to additional local production of turbulence (Chen et al., 2016) andsediment suspension (Caceres and Alsina, 2012). Cross shore gradients of combinedsuspended plus bedload transport rates are generally large and vary rapidly in time. This leadsto net deposition/erosion that varies along the swash zone and during the event: at the lowerswash zone, net erosion occurs during uprush and deposition during backwash, and patternsare opposite for the upper swash (Zhu and Dodd, 2015).
Knowledge on swash zone sediment transport processes is hampered by difficultiesencountered in obtaining detailed measurements in the challenging environment thatcharacterizes this zone (highly aerated flow, shallow water depths, large fluxes). In particular,only few studies managed to resolve intra swash event bed level changes (Puleo et al., 2014)and to obtain measurements of sheet flow layer processes (Lanckriet, 2014) in a medium sandswash zone. The bed level in the swash zone fluctuates at time scales of wave groups and ofshort waves. The net (=event averaged) bed level change is importantly affected by theduration of a swash event and the interruption of the backwash by incoming swash bores(Puleo et al., 2014). Lanckriet et al. (2014) showed that vertical profiles of sheet flowconcentrations during the backwash are similar to non breaking oscillatory flow observations.However, sheet flow layer thicknesses are significantly higher in the swash due to additionalfactors such as bore turbulence (Lanckriet and Puleo, 2015). These aforementioned studieswere done at natural beaches with irregular waves and it is anticipated that the understandingof sheet flow and bed level dynamics at intra swash time scale may benefit from systematiclaboratory experiments with repeating wave conditions and no longshore transport. Suchstudies may particularly assess the intra swash cross shore advection of sediment and theeffects of wave swash interactions on sheet flow dynamics and bed level changes.
1.3 Practical sand transport models
The term practical sand transport model is used for semi empirical models that are developed forapplication in engineering practice. These models generally operate at a wave averaged timescale and calculate transport rates based on relatively few hydrodynamic input parameters(e.g. Meyer Peter and Muller, 1948; Bailard and Inman, 1981; Nielsen, 1986; Ribberink, 1998;Van Rijn, 2007a; Van Rijn, 2007b). This opposes process based sand transport models, that describethe physics of sediment transport processes in much more detail, are used primarily as aresearch tool, and operate at an intra wave time scale (e.g. Hsu et al., 2004; Revil Baudard andChauchat, 2013; Kranenburg et al., 2014; Finn et al., 2016). Practical sand transport modelingapproaches for bedload and suspended load are notably different, as detailed below.
Chapter 1
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Bedload transport models
Many bedload transport models exist; for an overview, the reader is referred to recent reviewpapers (e.g. Van Rijn et al., 2013) or studies that inter compare these models (Davies et al., 1997;Davies et al., 2002). Most bedload transport models were developed and calibrated usingdatabases of transport rates under uniform conditions in tunnels or wave flumes (with nonbreaking waves) (e.g. van der Werf et al., 2009). Many classical bedload models assumetransport to respond quasi instantaneously to wave forcing. More recently, models have beendeveloped that use a semi unsteady concept that allows the inclusion of phase lag effects ontransport under waves (Dibajnia and Watanabe, 1992; van der A et al., 2013). Inmorphodynamic models that operate on a wave averaged time scale, the intra wave velocitystatistics (skewness, asymmetry, peak onshore and offshore velocities) required as input forbedload models are estimated through parameterizations (e.g. Isobe and Horikawa, 1982;Ruessink et al., 2012).
Suspended sediment transport models
Suspended sediment transport in a morphodynamic model is commonly calculated throughwave averaged advection/diffusion models. The advection term represents the horizontalcurrent related transport, i.e. the product of wave averaged velocities and concentrations. Thediffusion term represents the turbulent sediment fluxes in horizontal and vertical direction,which are modelled as a diffusive process using expressions for the sediment diffusivity thatare either purely empirical or based on (separately calculated) turbulent viscosities. Sedimentconcentration profiles follow from the advection/diffusion rates plus contributions by verticalsettling and exchange with the bed (pick up/deposition).
Vertical exchange between suspension and the bedload layer can be modeled using pick uprate functions or through a reference concentration close to the bed. Such pick up/referenceconcentration models are usually based on horizontal bed shear by waves plus currents andhave been developed based on measurements for non breaking waves (e.g. Nielsen, 1986; VanRijn, 2007b). However, these models have limited predictive capability in breaking waveconditions due to additional breaking related processes (Aagaard and Jensen, 2013). Referenceconcentration/pick up formulations that include a parameterization for breaking wave effects,e.g. through breaking wave parameters (Mocke and Smith, 1992; Kobayashi and Johnson,2001) or turbulent kinetic energy (Steetzel, 1993), have been proposed. However, theseformulations are not as thoroughly supported by experimental data and are not as widelyapplied as formulations based on horizontal bed shear.
The near bed wave related suspended transport can be included as part of the ‘near bed’ load(van der A et al., 2013) or as an additional term to suspended load transport (e.g. Van Rijn,2007b). The wave related load is considered importantly affected by wave skewness andasymmetry. An enhancement factor for wave related fluxes due to wave breaking has beenproposed (Van Rijn, 2007b), but this is not supported by a wide range of observational data(see Section 1.2).
Introduction
29
Swash zone
Several studies (see Chárdon Maldonado et al., 2015, for an overview) showed the limitedapplicability of bedload/total load formulas developed originally for uniform conditions whenapplied in swash zone conditions. This can be attributed to the importance of additionalprocesses, such as bore turbulence, infiltration/exfiltration, and large time varying cross shorepressure gradients, that are not commonly incorporated in sand transport models.O Donoghue et al. (2016) showed that for ‘free’ swash events, i.e. single swash events with nowave swash interactions, existing transport models can predict the time varying transportrates in the swash zone reasonably well. Previous studies have proposed transport modelsincorporating additional effects of turbulence on bed shear (Aagaard and Hughes, 2006) ordirectly on sediment transport (Butt et al., 2004), but this has not led to a unified swash zonetransport model.
Because of the limited predictive capability of transport models in the swash zone, somemorphodynamic models do not explicitly calculate sediment transport rates at grid pointscovering the swash. Instead, sediment transport rates are calculated up to the ‘wet’ grid pointnearest to the shoreline. This transport yields an erosion or accretion rate which is then spreadover the ‘wet’ and ‘dry’ cell adjacent to the shoreline (e.g. Delft3D, see Deltares, 2015a), or overthe complete swash zone (i.e. up to maximum run up distance) (Walstra and Steetzel, 2003;Van Rijn, 2009). However, these schematizations neglect many important physical processesand do not always yield satisfactory results (Van Rijn et al., 2011).
1.4 Problem statement and research questions
Present morphodynamic models fail at simulating long term beach morphology, unless inputparameters are heavily calibrated (Van Rijn et al., 2013). This is partly attributed to theinaccuracy of practical sand transport models in breaking wave and swash zone conditions.There is no unified view on how processes as flow non uniformity, enhanced turbulence dueto wave breaking, and wave swash interactions, should be incorporated in existing modelformulations for bedload and suspended transport in breaking and swash zone. Formulationsthat account for breaking wave effects on sediment transport have been proposed (Section1.3), but are not supported by detailed processes measurements of sand transport processes inthe breaking and swash zone.
The inaccuracy of sand transport model predictions reflects the still incomplete understandingof how wave breaking and swash zone processes affect sediment transport. Specific sedimenttransport processes have not yet been studied in detail, predominantly because highresolution measurements of these processes are lacking (Section 1.2). Many of the previousstudies on wave breaking were done in small scale wave flumes, which cannot give completeinsights in the effects of wave breaking on near bed hydrodynamics, since they do notreproduce the turbulent scales and turbulent wave bottom boundary layer of full scaleconditions. Previous observations of turbulence and suspended sediment in large scalefield/laboratory surf zones did not cover the wave bottom boundary layer at all or only withlow spatial resolution. In addition, previous studies did not allow examination of cross shoreadvective transport processes because the breaking region was not sampled with large
Chapter 1
30
horizontal coverage. The few swash zone studies that address intra swash bed level changesand sheet flow processes were conducted in the field and it may be expected that controlledwave flume experiments can further unravel effects of specific swash zone processes (e.g.wave swash interactions, cross shore intra swash sediment advection) on sediment transport.
Altogether it is concluded that present understanding of near shore sediment transport isparticularly hampered due to a lack of high resolution measurements of the followingprocesses:
The wave bottom boundary layer flow and time varying near bed (breakinggenerated) turbulence under large scale breaking waves;
Bedload and suspended sediment transport processes under breaking waves, inrelation to breaking generated turbulence and the cross shore non uniformity of theflow in the breaking region;
The vertical and horizontal distribution of suspended and bedload fluxes and transportrates under breaking waves, and their contributions to breaker bar morphology;
Intra swash event bed level changes and sheet flow processes in the swash zone undercontrolled laboratory swash events.
Novel instruments enable much higher resolution measurements of the wave bottomboundary layer and the sheet flow layer than previous studies. These instruments are used inthe present study to further explore sediment processes in the surf and swash zone. Hence,the main objective of this study reads:
To improve understanding of sediment transport processes and morphodynamics in thesurf and swash zone through high resolution measurements in large scale laboratoryconditions.
This objective is assessed through four research questions (RQs):
RQ 1) How does wave breaking affect near bed (wave bottom boundary layer) flow andturbulence?
RQ 2) How are suspended sediment transport processes affected by wave breaking?
RQ 3) How are bedload processes affected by wave breaking and how do suspended and bedloadtransport contribute to breaker bar morphodynamics?
RQ 4) How do swash processes such as wave swash interactions and cross shore intra swashadvection of sediment affect bed level changes and sheet flow layer dynamics?
1.5 Methodology
All research questions are addressed through high resolution sediment transport processmeasurements during experiments in the large scale CIEM wave flume at the UniversitatPolitècnica de Catalunya, Barcelona (Figure 1.4). The scale of this wave flume allows toreproduce the physics at the same scale as natural processes in the field. Compared toobservations in the field, wave flumes offer the major advantage that experiments can beexactly repeated as bed profile and wave conditions are controlled (reproducibility). This
Introduction
31
improves confidence in the results, as measurements can be ensemble averaged overnumerous wave cycles that are almost identical. In addition, processes of interest can beexamined in isolation, i.e. effects of other processes that are not subject of investigation can beomitted or minimized. In the present study, for example, effects of longshore flow and of timevarying wave conditions (tides, infra gravity waves) are omitted.
Data are collected during two experimental campaigns: one focusing on surf zone, the otheron swash zone processes. Both campaigns focus on detailed hydrodynamics and sedimenttransport processes, with particular interest on the near bed region, in relation to the largerscale morphology of the bed profile. Of particular relevance in this thesis are data collectedwith two novel instruments (Figure 1.4c): an Acoustic Concentration Velocity Profiler (ACVP;Chapters 2 and 3) and an upgraded Concentration Conductivity Measuring system (CCM+;Chapters 4 and 5). These novel instruments allow high resolution measurements of processesthat could not be studied in such detail before.
Figure 1.4. Photos of experiments in CIEM wave flume. (a) Plunging breaking waves, observed frommobile trolley above the flume while facing offshore (towards wave paddle); (b) Mobile measuring
frame plus equipment, seen from inside flume (while partly filled); (c) Sandy bed profile duringSINBAD mobile bed campaign, including novel instrumentation: ACVP (Chapters 2 and 3) and CCM+
(Chapters 4 and 5).
RQs 1 to 3 are answered through large scale experiments involving regular plunging wavesabove a mobile medium sand bed profile consisting of a bar plus trough configuration. Abreaker bar and trough are naturally formed at sandy beaches. This topography is expected tohave an important effect on controlling hydrodynamics and sediment transport dynamics andis therefore preferred over a horizontal bed or a plane sloping beach. The experiment involvesone monochromatic wave condition and has a duration of 90 min during which the bed profile
Chapter 1
32
evolves. A high spatial coverage of measurements is achieved by repeating the experiment 12times while measuring at different cross shore locations. This in depth exploration of onewave condition allows to study the spatial variation in hydrodynamics and sedimentprocesses, and is therefore preferred over an experiment with a wide range of wave conditionsbut with limited resolution. It is also anticipated that the in depth exploration of a single wavecondition will be of more benefit to process based numerical model development. The wavecondition is chosen such that the waves approach field conditions, result in energetic near bedflow (i.e. sheet flow) conditions, and break as a plunging type. The latter is preferred over aspilling breaker, because previous research showed a stronger temporal variability and largerpenetration depth of breaking generated turbulent kinetic energy under plunging breakingwaves.
RQ 4 is answered through another experimental campaign in the same wave flume, focusingon effects of wave group sequencing on beach morphology. During this campaign a newinstrument (CCM+) is applied for the first time. The CCM+ is used to study time varying bedlevel changes and sheet flow processes induced by energetic swash events with strong waveswash interactions. The present thesis highlights results of two selected bichromatic waveconditions.
The study presented in this thesis is embedded in a larger research project (‘SINBAD’) thatinvolves researchers from various European institutes. Next to experiments presented in thisthesis, an accompanying experiment involving breaking waves over a rigidized bed profilewas also conducted within SINBAD (Van der A et al., Submitted). Breaking wave effects onsediment transport are further explored within SINBAD using process based numericalmodels that simulate bedload transport processes and breaker bar morphodynamics, andthrough simulations with (engineering type) morphodynamic models. The experimental datawill be made available to the (external) scientific community once the project is finished.
1.6 Outline
Each of the four research questions (Section 1.4) is treated in a technical chapter (see Table 1.1for an overview). Chapter 2 addresses near bed hydrodynamics in the breaking region (RQ 1),with particular focus on temporal and spatial variations of turbulent kinetic energy. Chapter3 addresses suspended sediment transport processes (RQ 2) under breaking waves. Chapter 4is focused on bedload processes under breaking waves and also discusses the contributions bybedload and suspended load to breaker bar morphodynamics (RQ 3). Sheet flow and bed leveldynamics in the swash zone (RQ 4) are presented in Chapter 5. Chapter 6 presents a discussion,addressing the limitations of the present research, but also giving suggestions on how thepresented results can help improving practical sand transport models. Finally, Chapter 7contains the main conclusions from the study and recommendations for future research.
Introduction
33
Table 1.1. Outline of the thesis.
Chapter Research Question Experimental campaign
2RQ1) Breaking waves:near bedhydrodynamics
‘SINBAD mobile bed’Large scale measurements of breaking waves over
a medium sand barred bed profileCIEM, Barcelona, May/June 2014
3RQ2) Breaking waves:suspended sedimentprocesses
4RQ3) Breaking waves:bedload processes andmorphology
5RQ4) Swash zone:sheet flow and bedlevel changes
‘CoSSedM’ (Alsina et al., 2014)Coupled High Frequency Measurement of Swash
Sediment Transport and MorphodynamicsCIEM, Barcelona, Oct Dec 2012
Chapter 2
34
2 Near bed hydrodynamics andturbulence below a large scaleplunging breaking wave over amobile barred bed profile
Highlights
Breaking induced turbulence spreads over the full water column and invades the wavebottom boundary layer.
Reynolds stresses and TKE values in the wave boundary layer increase substantiallyin the breaking zone.
An increased wave boundary layer thickness is observed in the breaking region alongthe breaker bar’s shoreward slope.
Near bed hydrodynamics under a plunging wave
35
Abstract
Detailed measurements are presented of velocities and turbulence under a large scale regularplunging breaking wave in a wave flume. Measurements were obtained at 12 cross shorelocations around a mobile medium sand breaker bar. They focused particularly on thedynamics of the wave bottom boundary layer (WBL) and near bed turbulent kinetic energy(TKE), measured with an Acoustic Concentration and Velocity Profiler (ACVP). The breakingprocess and outer flow hydrodynamics are in agreement with previous laboratory and fieldobservations of plunging waves, including a strong undertow in the bar trough region. TheWBL thickness matches with previous studies at locations offshore from the bar crest, but itincreases near the breaking wave plunge point. This relates possibly to breaking induced TKEor to the diverging flow at the shoreward slope of the bar. Outer flow TKE is dominated bywave breaking and exhibits strong spatial variation with largest TKE above the breaker barcrest. Below the plunge point, breaking induced turbulence invades the WBL during both crestand trough half cycle. This results in an increase in the time averaged TKE in the WBL (by afactor 3) and an increase in peak onshore and offshore near bed Reynolds stresses (by a factor2) from shoaling to breaking region. A fraction of locally produced TKE is advected offshoreover a distance of a few meters to shoaling locations during the wave trough phase, and travelsback onshore during the crest half cycle. The results imply that breaking induced turbulence,for large scale conditions, may significantly affect near bed sediment transport processes.
__________________________________________________________________________________
This chapter has been published as:
van der Zanden, J., D. A. van der A, D. Hurther, I. Cáceres, T. O Donoghue and J. S.Ribberink (2016). Near bed hydrodynamics and turbulence below a large scale plunging breakingwave over a mobile barred bed profile. Journal of Geophysical Research: Oceans 121(8): 64826506. doi: 10.1002/2016jc011909.
Chapter 2
36
2.1 Introduction
Motivated by the need to improve understanding of cross shore sediment transport processesin the near shore region, a number of laboratory (e.g. Ting and Kirby, 1994, 1995; Yoon andCox, 2010) and field (e.g. Ruessink, 2010; Feddersen, 2012) studies have addressed the effectsof wave breaking on hydrodynamics. Many of these studies focused on the temporal andspatial distribution of breaking induced turbulence, since turbulent vortices have the potentialto entrain and stir sediment particles (Sumer and Oguz, 1978). While wave breaking ishighlighted as the dominant source of turbulent kinetic energy (TKE) production in the surfzone (Thornton and Guza, 1983; Ruessink, 2010; Yoon and Cox, 2010), bed friction generatedturbulence can contribute importantly to turbulence in the lower water column (Feddersen,2012; Brinkkemper et al., 2015).
Turbulence production and transport mechanisms depend on breaker type (Ting & Kirby,1994). In the case of a plunging breaker (the focus of the present study), turbulent vortices areformed at the wave front (Kimmoun and Branger, 2007; Sumer et al., 2013) and a major part ofthe breaking induced TKE is dissipated within the turbulent bore above wave trough level(Svendsen, 1987; Govender et al., 2002). The remainder is injected into the water column andis advected shoreward and downward by the plunging jet and large scale vortices (Ting andKirby, 1995; Christensen and Deigaard, 2001; Melville et al., 2002; Kimmoun and Branger,2007). Turbulent dissipation rates under breaking waves have been found to be depth uniform(Grasso et al., 2012) or to decrease with depth (Feddersen and Trowbridge, 2005; Yoon andCox, 2010), leading to a general reduction of TKE from the water surface downwards (e.g.Ruessink, 2010). Despite the dissipation of breaking induced turbulence over the watercolumn, a fraction may still reach the near bed region (Grasso et al., 2012). TKE profiles havebeen found to vary in the cross shore direction and depend on the bed topography, withhighest TKE found at the breaker bar crest and lower TKE above the bar trough (Scott et al.,2005; Yoon and Cox, 2010).
Small scale experiments revealed strong phase dependency of TKE under plunging breakers,with highest values during the wave crest phase for a major part of the water column (Tingand Kirby, 1995; Govender et al., 2002). Depending on breaker characteristics and local waterdepth, this phase dependency may reverse near the bed (Boers, 2005). It is believed that thephase dependency of breaking induced TKE is coherent with near bed wave related sedimenttransport (Ting and Kirby, 1994; Boers, 2005; Ting and Nelson, 2011).
While significant attention has been paid to hydrodynamics in the breaking region, few studieshave focused on the wave bottom boundary layer (WBL) under breaking waves. Breakinginduced vortices may invade the WBL (Cox and Kobayashi, 2000; Huang et al., 2010;Chassagneux and Hurther, 2014) and can substantially enhance near bed TKE (Scott et al.,2005) and bed shear stresses (Deigaard et al., 1991; Cox et al., 1996; Sumer et al., 2013). Most ofthese studies were conducted in small scale wave flumes (mostly over rigid, planar slopingbeds), which may not fully reproduce the properties of breaking induced turbulence and ofthe WBL hydrodynamics under full scale waves. To the authors’ knowledge, previous largescale experiments have not produced high resolution measurements within the WBL acrossthe wave breaking region. Such measurements are important for better understanding of wavebreaking effects on sediment transport processes.
Near bed hydrodynamics under a plunging wave
37
This paper studies the hydrodynamics under large scale, plunging breaking waves above amobile sand barred bed profile. The paper particularly addresses how wave non uniformityand wave breaking affect the near bed hydrodynamics, including the WBL.
The experimental conditions, details of instrumentation, and data processing procedures arepresented in Section 2.2. Measurements of the breaking process and outer flow velocities arepresented in Section 2.3. Section 2.4 presents the time averaged and phase averaged near bedvelocities and Section 2.5 presents the spatial and temporal variability of near bed turbulence.The wave breaking effects on the WBL hydrodynamics and the implications for sedimenttransport processes are discussed in Section 2.6.
2.2 Experiments
2.2.1 Facility and test conditions
The experiments were carried out in the 100 m long, 3 m wide and 4.5 m deep CIEM waveflume at the Universitat Politècnica de Catalunya (UPC) in Barcelona. The experimental setup and bed profile are shown in Figure 2.1. In this figure and throughout the document, thecross shore coordinate x is defined positively towards the beach with x = 0 at the wave paddle.Vertical coordinate z is defined positively upwards from the still water level (SWL); is thevertical coordinate from the local bed level upwards.
The initial bed configuration (i.e. before the waves developed the barred beach) comprised a1:10 offshore slope, followed by an 18 m long and 1.35 m high horizontal test section (Figure2.1a). The bed profile consisted of sand with median diameterD50= 0.24 mm. Shoreward of thetest section (x>68.0 m), the profile followed a 1:7.5 slope covered with geotextile and perforatedconcrete slabs designed to prevent erosion and promote wave energy dissipation. The waterdepth, h, at the wave paddle was 2.55 m.
Regular (monochromatic) waves were generated with wave period T = 4.0 s and wave heightH = 0.85 m at the wave paddle. The surf similarity parameter is 0 = 0.54, where
0= tan ( )/ H/L0, being the 1:10 offshore slope and L0 the deep water wave length (Battjes,1974). The breaking waves were of the plunging type, in agreement with the classification ofBattjes (1974).
Figure 2.1b indicates the breaking point (x = 53.0 m), the plunge point (x = 55.5 m) and thesplash point (x = 58.5 m). These points were established from measurements and visualobservations of the water surface, as described further in Section 2.3.1, and are used to definethe shoaling region (x < 53.0 m), the breaking region (53.0 < x < 58.5 m) and the inner surf zone(x > 58.5 m).
Chapter 2
38
Figure 2.1: Bed profile and measurement locations. (a) General overview of wave flume, includinginitial horizontal test section (dotted line), reference bed profile (bold black line), fixed beach (solidgrey line) and locations of resistive wave gauges (black vertical lines); (b) Close up of test section,including instrument positions: mobile frame pressure transducer (PT mob.; white squares); wall
mounted PTs (black squares); mobile frame ADVs (stars); and ACVP profiles (grey rectangles).
2.2.2 Instrumentation
The primary instrumentation was deployed from a custom built mobile frame (Figure 2.2).The frame was constructed from 30 mm diameter stainless steel tubing and was designed tominimize flow interference while being sufficiently stiff to withstand wave forces. The framewas mounted to a horizontally mobile trolley on top of the flume, and could be verticallypositioned with sub mm accuracy using a spindle. More details of the measurement frame areprovided by Ribberink et al. (2014).
Outer flow velocities (i.e. higher than 10 cm above the bed) were measured using a verticalarray of three Nortek Vectrino acoustic Doppler velocimeters (ADVs, Figure 2.2). All ADVsoperated at an acoustic frequency of 10 MHz and provided 3 component (cross shore, lateral,and vertical, denoted u, v, and w, respectively) velocity measurements at a rate of 100 Hz. Thesampling volume is a cylinder shaped volume with 3 mm radius and 2.8 mm height. TheADVs were located at elevations of approximately 0.11 m, 0.41 m and 0.85 m above the initial(i.e. at start of run) bed.
Near bed velocities (i.e. below 10 cm above the bed) were measured using a downwardlooking High Resolution Acoustic Concentration and Velocity Profiler (ACVP, Figure 2.2inset), described in more detail in Hurther et al. (2011). The ACVP measures simultaneous andco located vertical profiles of (u, w) and sediment mass concentrations (Hurther et al., 2011),
0 10 20 30 40 50 60 70 80
z (m
)
-2.55-2
-1
0
H=0.85 m, T=4 sSWL
RWGsh0=2.55 m
ht=1.35 m
x
(a)
x (m)50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
z (m
)
-1.5
-1
-0.5
0
0.5(outer) breaking regionshoaling region inner surf zone
ACVP
ADV
PT (mob.) PT (wall)
ζ
zSWL breaking point plunge point splash point
(b)
Near bed hydrodynamics under a plunging wave
39
hereby providing the possibility to measure intra wave, multi directional sediment flux. In thepresent experiment, the ACVP acoustic and geometrical settings were set to measure velocitiesup to 1.8 m/s over a vertical profile of 20 cm with a vertical bin resolution of 1.5 mm, ahorizontal radius of the sampling volume of about 3 mm, and sampling frequency of 70 Hz.Operating at an acoustic frequency of 1 MHz, considerably lower than the frequency ofcommercial ADV technology, the ACVP enables velocity and concentration measurements tobe made within the near bed sediment layer (c.f. Naqshband et al., 2014; Chassagneux andHurther, 2014; Revil Baudard et al., 2015).
Figure 2.2. Photo of measuring frame, taken from top of breaker bar while facing the beach.Highlighted instruments: ADVs (orange circles); PT (yellow square); ACVP (blue rectangle). Inset
shows close up of ACVP.
Water surface elevations were measured at 40 Hz using resistive (wire) wave gauges (RWGs)and pressure transducers (PTs) at 21 locations along the flume (Figure 2.1) and one additionalPT attached to the mobile frame (Figure 2.2). In the breaking region the horizontal spacing ofthe measurements was approximately 1 m. In this region, PTs were deployed instead of RWGsbecause wave splash reduces the data quality of the RWGs. Linear wave theory was used toconvert the dynamic pressure measurements (PT) into water surface elevations. FollowingGuza and Thornton (1980), the conversion was applied to frequencies up to 0.33 Hz, whichincludes the primary wave component (0.25 Hz) but not its higher harmonics. A comparisonwith RWG measured water surface elevation in the shoaling zone indicated that the PT
Chapter 2
40
derived wave height underestimates the RWG measured wave height by up to 10%. Theunderestimation in higher order statistics (wave skewness, asymmetry) is more severe.
Bed profile measurements were obtained along two transects, using echo sounders deployedfrom a second mobile carriage, at a horizontal resolution of 2 cm and with an estimated bedmeasurement accuracy of +/ 1 cm. The transects were taken at a lateral distance of 0.1 m and0.7 m with respect to the flume’s centerline. Bed profiles presented in this paper are based onthe average of the two transects.
Table 2.1. Measured water level and velocity statistics at all measurement locations (t=0–15 min.): localwater depth (h); local bed slope at start experiment ( ); wave height (H); time averaged horizontal
velocity ( ); peak onshore and offshore phase averaged horizontal velocities (uon and uoff); semiexcursion length (a = 2T rms/2 ); Non dimensional semi excursion length a/ks, with roughness ks
estimated based on grain size and measured ripple dimensions using formulations by Van der A et al.(2013); Velocity skewness (Sk(u) = u3/urms
3 ); Velocity asymmetry (Asy(u) = – (u)3/urms3 , where is the
Hilbert transform (e.g. Ruessink et al., 2011); Reynolds number (Re = a on/ ; where kinematic viscosity= 1.0 10 6 m2/s). Velocity based variables are based on measurements from the lowest ADV ( =0.11
m).
x(m)
h(m) (°)
H(m) (m/s)
uon(m/s)
uoff(m/s)
a(m)
a/ks/103 Sk(u) Asy(u) Re/105
51.0 1.10 4 0.79 0.13 1.04 0.83 0.54 2.3 0.61 0.68 5.6
53.0 0.97 3 0.74 0.22 0.80 0.94 0.48 2.0 0.44 1.01 4.5
54.5 0.88 2 0.64 0.19 0.84 0.85 0.47 2.0 0.50 0.82 4.0
55.0 0.88 6 0.60 0.24 0.78 0.90 0.47 2.0 0.48 0.76 4.2
55.5 0.97 13 0.51 0.23 0.57 0.83 0.39 1.6 0.36 0.75 3.3
56.0 1.10 11 0.50 0.30 0.25 0.82 0.31 1.3 0.06 0.77 2.6
56.5 1.19 10 0.53 0.51 0.05 0.83 0.25 1.0 0.67 0.76 2.1
57.0 1.24 4 0.48 0.54 0.02 0.78 0.23 1.0 0.95 0.58 1.8
58.0 1.28 1 0.47 0.46 0.01 0.71 0.21 0.03 0.82 0.79 1.5
59.0 1.28 1 0.43 0.36 0.13 0.71 0.23 0.03 0.39 0.88 1.7
60.0 1.26 2 0.42 0.36 0.17 0.66 0.24 0.03 0.67 0.68 1.6
63.0 1.26 0 0.41 0.34 0.19 0.58 0.23 0.03 0.79 0.45 1.3
2.2.3 Measurement procedure
To create the reference bed profile for this experiment, regular waves (H=0.85 m, T=4 s) weregenerated for 105 minutes over the initial profile described in Section 2.2.1. Subsequently, the
Near bed hydrodynamics under a plunging wave
41
z (m
)
-1.5
-1
-0.5(a) t = 0 min.
z (m
)
-1.5
-1
-0.5(b) t = 30 min.
z (m
)
-1.5
-1
-0.5(c) t = 60 min.
x (m)45 50 55 60 65 70
z (m
)
-1.5
-1
-0.5(d) t = 90 min.
flume was slowly drained, bed forms and lateral bed asymmetries were flattened out, and theresulting barred profile was drawn on the flume sidewalls to give the template for thereference bed profile (Figure 2.1).
Each experiment was run for 90 minutes of waves, comprising of six 15 min runs, duringwhich the bed further evolved. The bed profile was measured at the start of each experimentand after every second run, i.e. at 0, 30, 60 and 90 min. After the sixth run, the flume wasdrained and the reference profile was restored by shoveling back the transported sand andflattening out any bed forms that were generated. This sequence of bed profile developmentand subsequent restoration to the reference profile was repeated 12 times (12 experimentaldays), where for each experiment the mobile frame was positioned at a different cross shorelocation (Figure 2.1b).
As a reference throughout the paper, Table 2.1 presents wave height, water depth, velocityand local bed slope measurements for each mobile frame measurement location.
Figure 2.3. Measured bed profiles for each measurement day. Each panel contains 11 profilemeasurements, taken at the same stage of profile development (data for one measurement day were
discarded due to calibration issues).
Chapter 2
42
2.2.4 Morphology and experimental repeatability
A prerequisite for combining the measurements from different cross shore locations into onedataset is that the experiment is repeatable in terms of wave conditions and bed evolution.Figure 2.3 shows a comparison of measured bed profiles at different stages of bardevelopment. The good agreement between the profiles confirms the repeatability of the bedevolution. The locations of the smaller bed forms varied with each repeat, but the dimensionsand growth rate of the main features of the profile – the breaker bar and trough – were verysimilar between experiments. The repeatability of bed profile evolution can be quantified bythe standard deviation over the 11 profiles at t = 90 min, which was 3 cm in the region 50.0 m< x < 67.0 m, including the variability due to smaller bedforms. Wave heights were also similarbetween experiments, with a standard deviation (calculated over 12 experimental days) inmean wave height per cross shore location of less than 2 cm (mean value over all RWGs andPPTs).
During the experiment, the breaker bar increased in height while its trough deepened (Figure2.3). The offshore slope before the bar crest gradually increased in steepness, up to a 1:8steepness after 90 min. The bar growth and steepening induces enhanced shoaling and anincrease in 0 (up to 0.68), resulting in an increasing plunging intensity throughout theexperiment.
Figure 2.3 indicates the presence of bedforms, starting at the lee (shoreward) side of thebreaker bar. Visual observations of the bed after draining the flume confirmed a gradualtransition of shoreward facing lunate shaped features in the bar trough (x = 57.0 to 59.0 m), toquasi 2D features (with short wave length in wave direction but long wave length in wavenormal direction; x = 59.0 to 62.0 m), to irregular 3D vortex ripples in the inner surf zone (x>62.0m). Quasi 2D bed forms were also observed at the lee side of the bar, where they progressivelymigrated offshore and upslope (Figure 2.3b c). At the bar crest, the absence of bed featuresindicates sediment transport in the sheet flow regime. Further down the offshore slope (x<48m), a region that is not further considered in the present study, quasi 2D mega ripples wereobserved.
2.2.5 Data treatment
This paper focuses on measurements obtained during the first run of each measurement day,i.e. for the first 15 min of profile development. Later stages of bar development showedqualitatively similar behavior in terms of hydrodynamic processes; data for these later stagesare included in the Reynolds stress results, which were averaged over the entire 90 minexperiment in order to minimize the statistical bias error.
Visual observations and water surface measurements showed that the location of wavebreaking varied in time during the first 5 min of each run. After this transient phase, thebreaking location stabilized, indicating that a hydrodynamic equilibrium was established.Data obtained during the first 5 min of each run were therefore discarded, leaving 10 minutesof data per run for quantitative analysis. Flume seiching induced a standing wave with anamplitude of O(cm) and a period of about 45 s that matches the natural frequency of the bodyof water in the flume when h=2.55 m. The standing wave was removed from the velocity and
Near bed hydrodynamics under a plunging wave
43
water surface level measurements by applying a high pass filter with a cut off frequency ofhalf the primary wave frequency (0.125 Hz).
ADV data were contaminated with noise, predominantly due to high bubble concentrationsin the breaking region and with signal dropout when measuring above the water level. ADVdata were considered as outliers wen the signal to noise ratio was <15 dB, or the correlationwas <50% for time averaged quantities or <80% for instantaneous (turbulent) quantities. Thecorrelation threshold was lower for time averaged quantities, because the averagingprocedure contributes to noise cancellation. Outliers in phase ensembles were identified if thevalue deviated by more than three times the standard deviation from the median at the givenphase. Identified outliers were removed from the time series and not substituted by othervalues. The percentage data points removed varied in the cross shore direction, from about10% in the shoaling and inner surf zone, up to 45% in the highly aerated water column underthe plunging wave.
For the ACVP measurements, a level was first assigned to each measurement bin based onthe measured wave averaged bed level. The continuous bed level was obtained from themaximum backscatter intensity, following Hurther and Thorne (2011). Horizontal and verticalvelocity measurements were transposed to bed parallel and bed normal velocities, using arotation angle that minimized the periodic component of bed normal velocities close to thebed (at = 0.03 m). This transposition was applied on a wave by wave basis. The mean rotationangle obtained with this method at the different cross shore positions was close to the localbed slope estimated from the mechanical bed profile measurements. For simplicity, we referto the bed parallel velocities as the ‘horizontal’ velocities and the bed normal velocities as the‘vertical’ velocities in what follows.
The phase averaged value of arbitrary variable is denoted with angle brackets and wascalculated from
< > t =1N
(t+ n – 1 T)N
n=1
(2.1),
where N represents the number of wave cycles. N was about 150 for the water surface andouter flow velocity measurements, and somewhat lower for the ACVP measurements(typically about 100, with a minimum of 40). The reason for this difference is that data werediscarded when the local bed eroded outside the ACVP maximal profiling range or accretedto distances within the first 5 cm of the ACVP profile. Phase averaged near bed velocities(ACVP) were calculated for each bin class with 1.5 mm bin size. To calculate the phaseaveraged quantities, reference zero up crossing of the waves were obtained from the RWG atx=47.6 m. Data were then phase referenced such that t/T=0 corresponds to maximum watersurface (wave crest) at the beginning of the test section (x=50.0 m).
The quasi 2D bedforms observed in the breaking zone had cross shore wave lengths that were(much) higher than the local orbital amplitude a. Hence, it may be assumed that thesebedforms do not induce flow separation and do not contribute to apparent wave related bedroughness (Van Rijn, 2007a). The latter is not true for the inner surf zone (x>59.0 m), wherebedforms migrated below the ACVP sensors. For these locations, time intervals for phaseaveraging of ACVP measurements were chosen such that an integer number of bedforms was
Chapter 2
44
captured (i.e. the presented data are averaged over exactly one or multiple ripples) and =0corresponds to the time varying bed interface of the bedform.
Velocities were decomposed into time averaged ( ,w), periodic (u w) and turbulent (u’, w’)contributions. Time averaged quantities are denoted with an overbar and were calculatedusing
=1T
< t >dtT
0
(2.2)
For the discontinuous velocity measurements above wave trough level, represents thetruncated mean based on the ‘wetted period’ instead of the full wave period for T in Equation2.2. The periodic component is obtained from = < > – . Root mean square magnitudes of
are denoted with subscript rms and are calculated through:
rms=1T
t 2dtT
0
0.5
(2.3).
Various methods exist to extract the turbulent component from the time series (Svendsen,1987; Scott et al., 2005). The regular waves in the present experiment enable a Reynoldsdecomposition based on the ensemble average, i.e. ’ = – < >. Compared to other methods(see e.g. Scott et al., 2005), ensemble averaging yields the most accurate turbulence estimationssince it does not discard contributions of the largest vortices (Svendsen, 1987). However, byadopting this method, wave to wave variations due to offsets in phase referencing and as aresult of modulation of velocities and the breaking location by the long wave (flume seiching)may be incorrectly denoted as turbulence (Svendsen, 1987; Scott et al., 2005). These ‘pseudoturbulence’ contributions are largely suppressed through the aforementioned high pass filter(0.125 Hz). However, examination of the auto spectra of u’ and w’ revealed that the Reynoldsdecomposition removes most, but not all, of the energy associated with the wave and its higherharmonics (see Figure 2.A1). By integrating the auto spectra of u’with and without the energystill contained at the first three wave harmonic frequencies (0.25 Hz, 0.50 Hz, 0.75 Hz), it wasfound that the time averaged turbulence intensities are overestimated by approximately 7%.This error cannot be easily removed from turbulent velocity time series. The error is quitesmall compared to typical spatial and temporal variations of turbulence intensities in thisstudy and is therefore considered acceptable. The effect of wave bias on the Reynolds stresseswas separately tested using ogive curves (Feddersen and Williams, 2007) and led to theexclusion of 9 runs (as detailed in Appendix A).
Phase averaged rms turbulence intensities were calculated through
rms t =1N
( (t+ n – 1 T) < (t)>)2N
n=1
0.5
(2.4).
Estimates of < rms> are accepted only for N>40 to guarantee a low statistical bias error. Forthe 3 component ADV data, the TKE, noted k, can be calculated from the turbulence intensitiesthrough
Near bed hydrodynamics under a plunging wave
45
<k(t)> = 0.5(<u’(t)2> + <v’(t)2> + <w’(t)2>) (2.5).
Because of acoustic noise, the ACVP measurements were processed differently. A fullexplanation of the ACVP data processing is presented in Appendix A. In short, the acousticnoise was largely removed using a de spiking routine. Phase averaged turbulence intensitieswere then calculated using a two point cross correlation applied to velocities measured at twovertical bin elevations (Garbini et al., 1982; Hurther and Lemmin, 2001). <k(t)> was estimatedas 1.39 0.5(<u’(t)2> + <w’(t)2>), where the factor 1.39 is the typical value taken for a turbulentWBL (Svendsen, 1987). Contributions from small scale high frequency turbulent fluctuationsto turbulence intensities are partly removed using the methodology, leading to anunderestimation of TKE and Reynolds shear stress (Appendix A). The underestimationincreases towards the bed as the length scale of eddies reduces. Analyses in this study willtherefore exclude ACVP turbulence measurements within the lowest 5 mm from the bed.Finally it is noted that in dense suspension layers, the ACVP measures (turbulent) velocitiesof sand grains that may differ from the fluid velocities (Appendix A).
2.3 Water surface elevation and outer flow velocities
2.3.1 Surface elevation
The breaking process is examined by combining phase averaged RWG and PT measurementsof the water surface elevation (Figure 2.4). On arrival at the test section, the pitched forward,asymmetric shape of the wave is evident and is caused by wave shoaling along the offshoreslope. As the wave propagates towards the bar crest, the wave crest starts to turn over at x =53.0 m (at approximately t/T = 0.17). Following Svendsen et al. (1978), this location is referredto as the ‘breaking point’. As wave propagation continues, the plunging jet from the breakingwave hits the water surface approximately 2.5 m further at x = 55.5 m and at t/T=0.33 (‘plungepoint’, after Peregrine, 1983). The jet pushes up a wedge of water and creates a new wave thatleads the remainder of the original wave; the remainder of the original wave is called thesecondary wave in what follows. This breaking process, including the formation of thesecondary wave, is similar to detailed descriptions by Ting and Kirby (1995) for a small scaleplunging wave. While propagating further onshore, the water mass pushed up by theplunging wave hits the water surface around x = 58.5 m (t/T = 0.65). At this ‘splash point’ (Smithand Kraus, 1991), the wave reforms into a surface roller with a quasi uniform shapethroughout the remainder of the test section (x > 58.5 m). Based on these observations and afterSvendsen et al. (1978), we distinguish (see Figure 2.1) the shoaling zone (up to the breakingpoint at x = 53.0 m), the (outer) breaking zone (from breaking point to splash point; x=53.0 to58.5 m), and the inner surf zone (x>58.5 m).
The maximum (crest) and minimum (trough) phase averaged water levels are shown in Figure2.5, and can be used to analyze the cross shore variation in wave heightH (see also Table 2.1).The wave height gradually increases over the offshore slope as a result of wave shoaling(Figure 2.5a, up to x = 52 m). Wave energy dissipation starts near the breaking point at x = 53m and continues through the breaking zone; H is reduced by 50% between x = 52 m and x = 59m. The wave height decay drives a water level set up (preceded by a set down in the shoaling
Chapter 2
46
z (m
)
-1
-0.5
0
1 m/s
50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65t/T=0.08
z (m
)
-1
-0.5
0
jet hits water
t/T=0.33
z (m
)
-1
-0.5
0t/T=0.42
z (m
)
-1
-0.5
0t/T=0.50
z (m
)
-1
-0.5
0
surf boredevelops
secondary crestt/T=0.58
z (m
)
-1
-0.5
0t/T=0.75
x (m)50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
z (m
)
-1
-0.5
0
50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65x (m)
t/T=1.00
region), leading to a positive cross shore gradient in the mean water level throughout thebreaking and inner surf zone (Figure 2.5a).
Figure 2.4. Phase averaged water surface levels (PT and RWG, grey line plus dots) and velocities(ADVs) at selected phases. Horizontal grey lines mark the SWL ( =0) and the thick solid line at bottom
marks the reference bed profile.
Near bed hydrodynamics under a plunging wave
47
2.3.2 Outer flow velocities
Figure 2.5 shows vertical profiles of time averaged velocities (panel a) and rms periodicvelocities (panel b). Although ACVP (near bed) measurements are included in Figure 2.5a b,they are discussed separately and in more detail in Section 2.4.
Time averaged horizontal velocities (Figure 2.5a) are positive above wave trough level ( tr),highlighting an onshore mass flux, and are negative (offshore directed) below tr due to thecompensating return current (undertow). The undertow velocity magnitude increasesgradually in the shoaling zone (from x = 51.0 to 53.0 m) and more rapidly in the breakingregion, particularly along the lee side of the bar (Figure 2.5a). Maximum undertow velocitymagnitudes (up to 0.6 m/s) occur in the breaker bar trough (x = 56.5–58.0 m), similar toprevious studies involving barred profiles in field (e.g. Garcez Faria et al., 2000) and laboratory(e.g. Boers, 2005) conditions. In the inner surf zone (x > 58.5 m), undertow velocity magnitudesreduce. Over the bar crest (x = 55.0 m), highest offshore velocities occur in the middle of thewater column while at locations around the bar lee side and bar trough the highest offshorevelocities occur close to the bed (x = 56.5–59.0 m). A more in depth analysis of the undertowprofiles is not considered in the present study, which focuses primarily on the near bedvelocities.
Figure 2.5. Profiles of (a) undertow and (b) rms periodic velocities, both for t = 0–15 min., measuredwith ADV (squares) and ACVP (dotted profiles). Both panels include the cross shore varying wavetrough and crest level (black dots and dashed line) and the time averaged water surface level (set
up/set down; black dots and solid line).
50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
z (m
)
-1.5
-1
-0.5
0
0.5
SWL
ηtrough
η
ηcrest
u
1 m/s
(a)
x (m)50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
z (m
)
-1.5
-1
-0.5
0
urms~
1 m/s
(b)
Chapter 2
48
Root mean square horizontal periodic velocities ( rms) are nearly uniform with depth (Figure2.5b), as can be expected in shallow water. Measurements above trough level are notconsidered, because rms is undefined when data are discontinuous. rms is roughly constantbetween x = 51 and 55 m, decreases rapidly between x = 55 to 57 m, and varies hardlythroughout the inner surf zone (x > 58.5 m). The strong reduction in rms (x = 55 to 57 m) isconsistent with the decay of wave energy and the increased water depth in this region. Thedistinct near bed increase in rms towards the bed at all locations (most evident from x = 51 to55 m) relates to the velocity overshoot in the WBL which will be discussed further in Section2.4.2.
Figure 2.4 shows ADV measured phase averaged velocities at selected wave phases. As thewave arrives at the test section and travels along the offshore slope and bar crest (x = 51 to 55m), velocities are in phase with the water surface elevation, i.e. directed onshore under thewave crest and offshore under the wave trough. At wave plunging (t/T = 0.33), strong upwarddirected velocities under the wave front are evident and agree with earlier observations (e.g.Ting and Kirby, 1995). At the lee side of the breaker bar, the wave orbital motion interacts withthe strong undertow. At this location, velocities are directed offshore through almost thecomplete wave cycle. As the wave crest passes (t/T = 0.42 to 0.58), near bed velocities becomenearly zero due to the counteracting offshore directed return current and the onshore directedorbital crest velocities. During the wave trough phase (t/T = 0.75 to 0.2), the combination of thestrong undertow and negative orbital velocities results in strong offshore and upwardvelocities along the bar’s lee side.
2.4 Near bed and wave bottom boundary layer (WBL) flow
2.4.1 Phase averaged velocities
Figure 2.6 shows profiles of ACVP measured phase averaged horizontal velocities. Note thatthe bed was mobile and intra wave bed level variations occurred of O(mm). For consistency,
=0 m is set as a constant position for the entire wave cycle equal to the highest intra wave bedlevel. This level generally occurs around near bed flow reversal (zero velocity). Due to intrawave erosion of the immobile bed level, non zero velocities can be found at <0 m. As a proxyfor the maximum crest phase WBL thickness we introduce , defined as the elevation ofmaximum periodic velocity at the instance of maximum free stream velocity (following e.g.Jensen et al., 1989). Note that does not need to coincide with the elevation of maximum phaseaveraged velocities <u> in Figure 2.6, as these include the time averaged velocity contribution
.
At the four locations at the offshore slope of the bar (x =51.0 – 55.0 m), the profiles show similarbehavior (Figure 2.6). Since waves are strongly asymmetric (i.e. acceleration skewed), thetrough to crest half cycle is of shorter duration than the crest to trough half cycle. The highestnear bed velocities, exceeding 1 m/s, occur at the most offshore location (x=51.0 m). Theovershooting of velocities close to the bed ( 0.02 m) is addressed in the next section.
Near bed hydrodynamics under a plunging wave
49
-1 0 1
ζ (m
)
0
0.02
0.04
0.06
0.08
0.1Shoaling region
x=51.0 m
-1 0 1
53.0 m
-1 0 1
Breaking region
54.5 m
-1 0 10
0.02
0.04
0.06
0.08
0.1
δ
55.0 m
-1 0 1
ζ (m
)
0
0.02
0.04
0.06
0.08
0.155.5 m
-1 0 1
56.0 m
-1 0 1
56.5 m
-1 0 10
0.02
0.04
0.06
0.08
0.1
δ
57.0 m
<u> (m/s)-1 0 1
ζ (m
)
0
0.02
0.04
0.06
0.08
0.158.0 m
<u> (m/s)-1 0 1
Inner surf zone
59.0 m
<u> (m/s)-1 0 1
60.0 m
<u> (m/s)-1 0 1
0
0.02
0.04
0.06
0.08
0.1
δ
63.0 m
Figure 2.6. Vertical profiles of phase averaged horizontal velocity near the bed (ACVP; t=0–15 min.)for 10 phases evenly separated over the wave period. Distinction is made between trough to crest
half cycle (thin solid lines) and crest to trough half cycle (dotted lines). Thick solid lines correspond totimes of maximum onshore and offshore free stream velocity. Also included is the maximum
boundary layer thickness (horizontal dashed line).
Periodic velocities are lower along the shoreward facing slope of the bar and bar trough (x =55.5 – 58.0 m), consistent with the outer flow observations. At the same time, the offshoredirected return current (undertow) increases. The combined effect yields a reduction in crestvelocity magnitudes and in positive (onshore) velocity duration, especially from x = 56.5 to58.0 m, where velocities are negative (offshore) for almost the entire wave cycle. At somelocations (e.g. x = 56.0 m), velocities are increasingly directed offshore with distance from thebed as the magnitude of ( ) increases. These profiles are similar to those previously observedfor waves propagating against a steady current (e.g. Van Doorn, 1981; Kemp and Simons,1983). At x = 57.0 m, a positive d<u>/d is observed at elevations slightly above the WBL. This
Chapter 2
50
feature differs from previous wave current studies and relates to the large undertow velocitiesclose to the bed (Section 2.3; Figure 2.5a). At all locations, crest velocities at the elevation ofperiodic velocity overshooting ( = ) are larger than in the free stream ( = 0.10 m). This canlead to a short duration of onshore velocities at = , even when the free stream velocity isoffshore directed for the entire wave cycle (e.g. at x = 56.0 and 56.5 m).
In the inner surf zone, where the orbital velocity amplitude increases and the undertowmagnitude decreases (Figure 2.5; Table 2.1), the duration of onshore velocities graduallyincreases with x location (Figure 2.6). Compared to the shoaling and breaking regions, velocityprofiles in the inner surf zone are more depth uniform for > .
2.4.2 Time averaged velocities
Based on previous work, four main processes may affect time averaged velocities in the WBLin this experiment: (i) offshore directed undertow; (ii) onshore directed progressive wavestreaming (e.g. Kranenburg et al., 2012); (iii) wave shape streaming, offshore directed forpositively skewed/asymmetric waves (Trowbridge and Madsen, 1984; Fuhrmann et al., 2009b);(iv) flow convergence, leading to onshore directed near bed streaming at the seaward facingside of the breaker bar (e.g. Jacobsen et al., 2014).
Figure 2.7 presents the vertical profiles of time averaged horizontal velocities ( ) within andjust above the WBL. ( ) is presented both with linear (Figure 2.7a) and logarithmic (Figure2.7b) vertical axis, which allows a better comparison with previous WBL studies. All profilesin Figure 2.7 are scaled with the free stream velocity at =0.10 m.
For the most offshore location (x = 51.0 m), the profiles in Figure 2.7a b show four distinctsegments: (i) a logarithmic increase (in offshore direction) in from / = 0–0.5; (ii) a localmaximum (in offshore direction) between / = 0.5–0.8; (iii) a local minimum (in absolutesense) of between / = 0.8 and 1.8; and (iv) nearly depth uniform from / = 2–5. Theprofile shape is similar to previous observations under non breaking waves over a horizontalbed (Schretlen, 2012). Kranenburg et al. (2012) showed that this profile shape can be explainedthrough contributions of offshore directed wave shape streaming (segment ii) and onshoredirected progressive wave streaming (segment iii).
At all other cross shore locations (x>51 m), ( ) increases in magnitude with distance from thebed, with no evidence of wave shape or progressive wave streaming effects because of thestrong undertow. At some locations a double logarithmic velocity profile is observed, withinflection point above the WBL, as indicated by the blue lines at x=53.0 m (Figure 2.7b). Such
( ) profiles are typically observed in wave current conditions, obtained from numerical(Fredsøe, 1984; Davies et al., 1988) and experimental (Van Doorn, 1981; Kemp and Simons,1983) studies. At locations with particularly strong undertow relative to the orbital velocity,e.g. at x = 56.5 and 58.0 m (c.f. Table 2.1), the ( ) profiles follow a single logarithmicdistribution for elevations 0.5 < <2 (Figure 2.7b). This suggests that at these locations, nearbed velocities are dominated by the undertow with minor effect of wave induced mixing. Thedouble log profile seems to re establish at the inner surf zone, suggesting that the orbitalmotion regains importance in affecting the net currents.
Near bed hydrodynamics under a plunging wave
51
u/u0
-1 -0.5 0 -0.5 0 -0.5 0 -0.5 0 -0.5 0 -0.5 0 -0.5 0
ζ/δ
0
1
2
3
4
5x=51.0 m x=53.0 m x=55.0 m x=56.5 m x=58.0 m x=60.0 m x=63.0 m
(a)
u/u0
-1 -0.5 0 -0.5 0 -0.5 0 -0.5 0 -0.5 0 -0.5 0 -0.5 0
ζ/δ
0.1
0.2
0.5
1
2
5(b)
urms/u0,rms
0 0.5 1 0 0.5 1 0 0.5 1 0 0.5 1 0 0.5 1 0 0.5 1 0 0.5 1
ζ/δ
0
1
2
3
4
5
~ ~
(c)
x (m)50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
z (m
)
-1.4
-1.2
-1
-0.8(d)
Close to the bed ( <0.5 ), time averaged horizontal velocity profiles deviate from a logarithmicprofile. This occurs because =0 is defined as the level of the bed at rest, hence intra wave andtime averaged velocities may still persist at <0. In addition, for sheet flow conditions (x = 51.0to 55.0 m), velocities inside the sheet flow layer do not satisfy the logarithmic distribution(Sumer et al., 1996).
Figure 2.7. Near bed horizontal velocity profiles at selected locations. (a) Time averaged velocities; (b)similar to (a), but with vertical axis on logarithmic scale. The blue straight lines depict the velocitygradient, with inflection point that is typical for wave current interactions; (c) Root mean square
periodic velocities; (d) Reference bed profile at t=0 min. and measurement locations. All velocities in(a–c) are scaled with free stream velocities at =0.10 m.
2.4.3 Periodic velocities and wave bottom boundary layer thickness
Figure 2.8 shows the vertical profiles of horizontal periodic velocity < ( )> along the offshoreslope of the breaker bar. This figure differs from Figure 2.6 as time averaged velocities are
Chapter 2
52
subtracted. Overshooting occurs at each location during peak offshore and onshore phasesand is most prominent during the crest phase. The overshoot is explained by the velocity defectin the WBL behaving as a damped wave that travels upwards (Nielsen, 1992) and has beenobserved in boundary layers in oscillating flows (e.g. Jensen et al., 1989; van der A et al., 2011),under laboratory waves (e.g. Schretlen, 2012) and under laboratory spilling waves (Huang etal., 2010). Above = , peak onshore and offshore periodic velocity magnitudes graduallydecrease until a near zero vertical gradient is reached at 0.10 m. For all locations, the periodiccrest velocities at = are considerably (about 50%) higher than at 0.10 m. This is partlyattributed to a change in the shape of the periodic velocity time series as the bed is approached:changing phases of the higher harmonics leads to increasing velocity skewness and decreasingacceleration skewness (Berni et al., 2013). In the present experiment, this shape transformationstarts at 2–5 . Furthermore, the rms periodic velocities at = are notably higher than at0.10 m (Figure 2.7c and Figure 2.5b), leading to a larger orbital excursion and peak onshoreand offshore orbital velocities. Such increased rms at = relates to the velocity overshootingand is also observed at breaking and inner surf zone locations further shoreward (x > 55.0 m).In the present study, rms( )/ rms(5 ) 1.2 (+/ 0.1), which is somewhat higher than the value ofabout 1.07 found with numerical boundary layer models that were validated againstlaboratory observations for non breaking waves (e.g. Nielsen, 1992; Kranenburg et al., 2012).
Figure 2.8. Vertical profiles of phase averaged horizontal periodic velocity at shoaling locations for 20phases evenly spread over the wave cycle. Distinction is made between trough to crest half cycle (thin
solid lines), the crest to trough half cycle (dotted lines), and instances of peak crest and trough freestream velocity (thick lines).
The elevation of maximum periodic velocity overshoot during the crest phase is used here asa proxy of the WBL thickness (following Jensen et al., 1989). Previous measurements undervelocity skewed waves above a mobile bed showed that the overshoot elevation is at higherelevation during the crest phase than during the trough phase, i.e. when highest velocitymagnitudes are reached (Schretlen, 2012). In contrast, for positive acceleration skewed flows,the WBL thickness is smaller during the crest phase since the WBL has less time to developcompared to the trough phase (van der A et al., 2011). Comparison of the peak onshore andoffshore periodic velocity profiles (Figure 2.8) shows that the maximum overshoot elevationoccurs at a similar level for the crest and the trough phases. A possible explanation is that the
<u> (m/s)-1 0 1
ζ (m
)
0
0.02
0.04
0.06
0.08
0.1
~
x=51.0 m
<u> (m/s)-1 0 1
~
53.0 m
<u> (m/s)-1 0 1
~
54.5 m
<u> (m/s)-1 0 1
0
0.02
0.04
0.06
0.08
0.1
δ
~
55.0 m
Near bed hydrodynamics under a plunging wave
53
opposing effects of velocity and acceleration skewness on WBL thickness tend to cancel eachother out. Approximately similar crest and trough WBL thicknesses were also found at otherlocations in the breaking and inner surf zones (not included in Figure 2.8).
Measurements of are compared quantitatively with the empirical formulation of Fredsøe andDeigaard (1992):
/ks = 0.09(a/ks)0.82 (2.6),
in which ks denotes the roughness. Although Equation 2.6 was based on rigid rough bedexperiments, it has been shown to predict reasonably well WBL thickness for mobile bed sheetflow conditions for a range of sediment sizes in full scale oscillatory flows (O’Donoghue andWright, 2004a; Campbell et al., 2007) and non breaking progressive surface waves (Schretlen,2012). In these studies, the roughness was taken as 2.5D50 rather than relating ks to the sheetflow thickness. Hence, the roughness ks is here also set equal to 2.5D50.
Figure 2.9. Overshoot elevation ( ), as proxy for WBL thickness, along test section. (a) Dimensional ;(b) /a at = ; (c) Bed profiles at start (solid) and end (dashed) of experiment. Values depicted in (b)
and (c) are averaged over six runs per location (crosses and black line), with error bars marking +/ onestandard deviation of mean. The grey dots and dashed line in (a) and (b) mark the empirical
prediction by Equation 2.6 (Fredsøe and Deigaard, 1992).
Equation 2.6 is applied here in a situation with a superimposed current. This can be justifiedbased on the results of Nielsen (1992) who analyzed the dataset of van Doorn (1981) and foundno effect of a moderate strength superimposed current on rms periodic velocities (this isfurther discussed in Section 2.6). Equation 2.6 is applied only for flat bed locations, as rippledbed conditions are considered outside the equation’s application range.
δ (m
)
0
0.01
0.02
0.03
δ=0.09ks(a/ks)0.82 bed forms
plunge point(a)
δ/a
0
0.05
0.1
δ/a=0.09(a/ks)-0.18
(b)
x (m)50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
z (m
)
-1.6
-1.4
-1.2
-1
-0.8
-0.6(c)
0 min.90 min.
Chapter 2
54
The cross shore variation in and predictions of using Equation 2.6 are shown in Figure2.9a. Note that the measured values are averaged over six runs per location and that due tovariability of between runs, values in Figure 2.9a may differ slightly from values depictedin Figures 2.6 and 2.8.
Between x = 51.0 and 55.0 m, is almost constant. This may be expected as the free streamvelocities show little cross shore variation (Figure 2.5c). The measured is in good agreementwith predicted from Equation 2.6 and, consequently, is in good agreement with fromprevious oscillatory flow mobile bed experiments. This suggests that flow non uniformityunder progressing surface waves over the sloping bed has little impact on the WBL thicknessacross the shoaling and breaking locations offshore from the bar crest.
Near the plunge point, along the shoreward slope of the breaker bar, increases slightly, eventhough the periodic velocity amplitude decreases in this region. Consequently, /a increasessubstantially shoreward from the plunge point ( Figure 2.9b). In addition, measured aresubstantially larger than predicted ; especially from x=56.0 to 57.0 m, where the differenceexceeds a factor 2. Possible physical explanations for this observation are given in Section 2.6.
Towards the bar trough, both and /a decrease again. Further into the inner surf zone, atx=63.0 m, increases due to an increasing bed roughness in the presence of sand ripples andthe associated ripple vortex regime.
2.5 Turbulence
2.5.1 Time averaged turbulent kinetic energy
Figure 2.10a shows vertical profiles of time averaged turbulent kinetic energy (TKE), Froude
scaled ( k/gh) to enable comparison with previous studies. An offset between the ADV and
ACVP measured TKE becomes apparent and is discussed further in Section 2.6. The downlooking ACVP could induce wake turbulence, leading to enhanced turbulence magnitudesnear the sensor. However, no local increase in TKE near the sensor becomes apparent from thefigure, and the effect is therefore assumed negligible compared to other sources of TKE.
In the outer flow, TKE decreases from the top of the water column downwards. This decay isconsistent with many previous breaking wave studies (e.g. Scott et al., 2005; Yoon and Cox,2010), and implies that turbulence production by wave breaking and the surf bore dominatesturbulence levels in the upper half of the water column. The cross shore evolution of TKE inthe middle of the water column shows an increase from shoaling zone towards the bar crest,followed by a decay of k in the inner surf zone. This pattern is consistent with previous studiesinvolving a barred profile (Boers, 2005; Scott et al., 2005; Yoon and Cox, 2010). High values atthe bar crest relate to wave breaking, while the decrease towards the bar trough and inner surfzone is attributed to an increase in water depth (turbulence spreads over a larger water mass)and reduced wave energy (Yoon and Cox, 2010).
At the bar crest, and in the middle of the water column, we find k/gh 0.043. This matches
well with the magnitude of about 0.04 reported for similar scale flume experiments involving
Near bed hydrodynamics under a plunging wave
55
z (m
)
-1.5
-1
-0.5
0
√k/gh
0.05
trough level(a)
ζ/δ
0
1
2
3
4
5
k
0.015 m2/s2
(b)
x (m)50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
k δ, m
ax (m
2 /s2 )
0
0.005
0.01
0.015
0.02
0.025
0.03
breaking regionshoaling region inner surf zone
plunge point
(c)
plunging (but irregular) waves (Scott et al., 2005; Yoon and Cox, 2010; Brinkkemper et al., 2015).
However, k/gh is substantially smaller compared to the plunging wave tests of Ting and
Kirby (1994) and Govender et al. (2002), who found values of about 0.08. In addition, both thesestudies found k profiles that were almost depth uniform, indicating less decay of TKE withdepth compared to the present study and other large scale experiments. These differences mayrelate to the smaller scale and the plane sloping bed geometry (i.e. no bar) of Ting and Kirby(1994) and Govender et al. (2002), leading to relative wave heights H/h near the plunge pointthat are substantially larger than in the present study.
Figure 2.10. Time averaged TKE, measured with ADVs (squares) and ACVP (dots). (a) Froude scaledTKE over complete water column; (b) close up of TKE profiles near the bed and in the WBL; (c)Maximum time averaged TKE measured in the WBL, mean (dots and dashed line) +/ standard
deviation of mean (error bars).
Figure 2.10b shows ACVP measured vertical profiles of k( ) inside the WBL, and Figure 2.10cshows the cross shore evolution of maximum TKE inside the WBL. Near bed k at the mostoffshore location (x = 51.0 m) is depth uniform and its magnitude in the WBL is much lowercompared to all other cross shore locations. Apparently, the amount of turbulence producedat the bed is small. Further shoreward (x = 53.0 m), kmagnitudes increase rapidly from the bedupwards, reach a maximum at around = 0.5 , and decrease at higher elevations. The shapeof this profile, with highest values close to the bed, is similar to previous measurements from
Chapter 2
56
rigid bed oscillatory boundary layer experiments where the main turbulence production wasdue to bed shear (e.g. Jensen et al., 1989; van der A et al., 2011). The decrease in k for < 0.5(Figure 2.10b, x = 53.0 m) is not consistent with results from rigid bed experiments, for whichthe highest values of k are typically found much closer to the bed. This difference may be dueto physical processes in mobile bed conditions, such as turbulence damping (Dohmen Janssenet al., 2001; Hsu et al., 2004) or reduced turbulent mixing efficiency in the dilute suspensionlayer above a dense bedload layer (Revil Baudard et al., 2015). However, instrumentlimitations (Appendix A) may also be a factor. The strong increase in k ,max at x=53.0 m relativeto x=51.0 m, for the complete near bed layer including the WBL (Figure 2.10c), is remarkablesince magnitudes of free stream velocities are similar at both locations (Table 2.1). Thissuggests that turbulence at x = 53.0 m is not only produced locally at the bed and that there isa significant contribution of breaking generated turbulence that arrives at this location.
In the breaking region at x = 55.0 and 56.0 m, the near bed k profiles are more depth uniformwithout a distinct maximum within the boundary layer. The vertical distribution and themagnitudes of k suggest that TKE generation by bed friction is small compared tocontributions of breaking induced turbulence. Magnitudes of TKE increase from shoaling tobreaking zone for the complete near bed region including the WBL (Figure 2.10c). Ofparticular note is the increase in k ,max near the plunge point around the breaker bar crest (afactor 2.7 increase from x=54.5 to 56.0 m), despite the strongly decreasing peak onshore andoffshore near bed velocities in this region (Table 2.1). The bed is plane in this region, whichexcludes an increase in TKE due to small scale bed forms. The strong undertow current atthese locations is expected to have a minor effect on local turbulence values. This was shownpreviously in experiments with waves and superimposed current for which k values were notmuch larger compared to the same waves without a current (c.f. Kemp and Simons, 1983).Hence, results indicate that the substantial increase in k ,max in the breaking zone is primarilycaused by breaking induced turbulence that invades the WBL.
In the bar trough (x=57.0–59.0 m), magnitudes of k ,max are significantly lower than at bar crestlocations but are nevertheless notably higher than in the shoaling zone (c.f. x = 51.0 m). Thelatter suggests that breaking generated turbulence still reaches the bed in the bar trough,despite the much larger vertical distance between water surface and bed compared to bar crestlocations. The vertical profile of near bed k( ) at x=58.0 m is almost depth uniform (Figure2.10b). The absence of a near bed increase in k( ) suggests that bed shear by orbital velocitiesdoes not add significantly to local TKE. However, bed shear by time averaged velocities(undertow) may result in similar depth uniform profiles (see e.g. Sleath, 1991) and maytherefore contribute to near bed TKE in the bar trough. Vertical profiles of k( ) in the inner surfzone (x>58.5 m) show that bed generated turbulence due to orbital velocity shear graduallyregains importance. Throughout the inner surf zone, k ,max increases due to increasing bedform roughness (Figure 2.10c).
2.5.2 Time varying turbulent kinetic energy
Figure 2.11 shows detailed measurements of <k> inside the WBL and in the layer immediatelyabove it ( / =0–5). A dominance of bed generated turbulence in near bed time varying <k>occurs at locations relatively far from the plunge point, i.e. at x 54.5 m and at x > 58.5 m. Atx=53.0 and 54.5 m, large turbulent events are formed at the bed during instances of peak trough
Near bed hydrodynamics under a plunging wave
57
and crest velocities. The bed generated TKE remains confined to the WBL at x=53.0 m, butappears to diffuse outside the WBL at x=54.5 m. Bed generated TKE at the inner surf zone(x>58.5 m) is particularly observed during the crest phase. Turbulence production at the bedoccurs due to the presence of vortex ripples in the inner surf zone which increase the bedroughness. At these inner surf zone locations, similar to x = 53.0 m, bed generated TKE remainslargely confined to the WBL.
Figure 2.11. Time varying turbulent kinetic energy <k> near the bed, measured by ACVP for t=0–15min. Free stream horizontal velocities at = are included in each panel as a reference.
Breaking generated turbulence affects time varying near bed <k> at locations close to theplunge point at x = 55.5 m. At x = 55.5 – 56.0 m, i.e. roughly below the plunge point and closeto the bar crest, <k> increases during the early crest phase (t/T=0.4–0.6). This increase occursrapidly and uniformly over the complete near bed layer, which indicates that the source isbreaking induced TKE that comes from above and mixes rapidly over the near bed layer. This
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58
peak in TKE lags the instance of the plunging jet hitting the water (at x = 55.5 m and t/T 0.33)by t 0.5 s ( t/T 0.1–0.2). At x = 56.0 m, <k> increases a second time during the wave troughphase (t/T=0–0.3), marking a second event of turbulence arrival. A trough phase increase inTKE can also be identified at x=55.5 m, particularly when focusing on elevations outside theWBL ( =4–5 ). Closer to the bed at x=55.5 m, bed generated turbulence merges with breakinginduced TKE, leading to maximum <k> values that are much higher than at offshore locationswith similar near bed velocities (x=53.0 to 55.0 m).
Offshore from the plunge point, at x=55.0 m, a sudden increase in TKE above the WBL duringthe end of the wave trough phase (t/T=0.2) can be identified. This increase is rather uniformover depth, suggesting that this TKE is not produced locally at the bed but relates instead tothe arrival of breaking induced turbulence. After passage of the wave crest (t/T=0.4), TKEdecreases depth uniformly. Shoreward from the region of high turbulence below the plungepoint, at x=56.5 m, <k> increases rapidly during the crest phase (t/T=0.4 to 0.5). Again, thedepth uniformity of this increase suggests that it is not due to local turbulence production atthe bed. Further shoreward, in the region covering the lower lee side of the breaker bar andthe bar trough (x=57.0–58.0 m), the limited temporal variation in TKE indicates that there islittle turbulence production by wave related bed shear and limited arrival of advectedbreaking induced TKE.
Due to strong cross shore gradients in near bed TKE, the temporal behavior seen in Figure2.11 is not fully explained by local processes, i.e. production at the bed or at the water surfaceand advection/diffusion in vertical direction only. Instead, we may expect significantcontributions of horizontal turbulence advection to the temporal variation in near bed TKE.The horizontal TKE advection is seen in Figure 2.12c, which shows the spatiotemporalvariation in TKE at =0.11 m. The continuously high near bed TKE magnitudes at x=55.5 and56.0 m stand out. Along the offshore slope of the bar (x=51.0–55.0 m), the highest TKE valuesare found during the zero up crossing of the surface elevation. This relates not only toproduction at the bed ( Figure 2.11), but also to the arrival of TKE generated below the plungepoint which is advected offshore by orbital and undertow velocities during the trough phase.The latter is identified as a patch of high TKE that travels offshore from the plunge point at x= 55.5 m to the shoaling zone at x 52.0 m (Figure 2.12c, grey arrow). After flow reversal topositive velocities, the arriving fluid at shoaling locations comes from x<52.0 m and isrelatively low in TKE. Consequently, net advection of TKE is onshore (white arrow in Figure2.12c) leading to a decrease in TKE at shoaling locations.
An excursion of TKE also occurs from the plunge point to onshore locations, although thehorizontal extent over which TKE is advected is much more restricted, and consequently, theeffect is much less apparent. In Figure 2.12c, the onshore excursion is observed as the patch ofhigh TKE at x = 55.0 56.0 moves slightly onshore to x=56.5 m around t/T = 0.4, and back offshorearound t/T = 0.6. The effect is also observed in Figure 2.11 as a depth uniform increase in <k>during this time interval. The reduced orbital amplitude and the strong offshore directedundertow velocity lead to a short duration of onshore directed phase averaged velocities inthis region, and consequently, restrict the onshore and downward transport of TKE along theshoreward slope of the bar.
Near bed hydrodynamics under a plunging wave
59
Figure 2.12. Surface plots of spatial (horizontal axis) and temporal (vertical axis) variation in (a) Watersurface levels; (b) Horizontal velocities at = ; (c) TKE, measured by ADV at =0.11 m; (d) Near bed
TKE, measured by ACVP, depth integrated over the lowest 0.10 m (knb). Dashed lines depict zerocrossings of . Arrows in panels c d are explained in main text. Panel (e) shows the reference bed
profile.
Figure 2.12d shows the spatiotemporal variation in depth averaged (over =0–5 ) near bedTKE (annotated knb), which resembles the behavior at =0.11 m. Hence, also in the WBL, crossshore advection of breaking generated turbulence has a significant effect on <k>. Differencesbetween Figure 2.12c,d are mainly attributed to contributions of bed generated turbulence toknb ( Figure 2.11).
2.5.3 Reynolds shear stress
Figure 2.13 shows the Reynolds shear stress (– <u’w’>) at = . The Reynolds shear stress at thebed ( =0) could not be resolved due to instrument limitations (Appendix A).
In the vicinity of the plunge point (at x=55.5 m +/ 0.5 m), peak onshore and offshore Reynoldsstresses are found to increase rapidly, with a factor two increase relative to x = 54.5 m. Theincrease is likely associated with the effects of breaking induced turbulence that reaches thebed, because peak onshore and peak offshore velocities decrease between shoaling andbreaking zone (Table 2.1). Indeed, the increase in onshore/offshore Reynolds stresses occurs
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in approximately the same region where TKE in the WBL was observed to increase (c.f. Figure2.10a). Further shoreward (x=56.5–57.0 m), Reynolds shear stresses are almost continuouslydirected offshore, similar to the near bed velocities at these locations. The time averagedReynolds stresses (crosses in Figure 2.13) are predominantly negative, which is explained bythe negative time averaged near bed velocities.
Figure 2.13. Near bed Reynolds stresses at = , averaged over t=0 90 min. (a) Time averaged (crossesand solid line) and phase averaged peak onshore and offshore (dots and dashed lines) Reynolds
stresses; (b) Bed profiles at t=0 min. (solid line) and t=90 min. (dashed line).
2.6 Discussion
Offsets between ADV and ACVP measured k can be seen in Figure 2.10a. Whether these shiftsare attributed to differences between ADV and ACVP measurement resolution, differences inacoustic frequencies and associated sensitivity to different particle sizes, slight differences insystem orientation relative to the local bed slope (ADV data have not been corrected) or eveninvalid TKE approximation for the 2C velocity measurement of the ACVP (see Section 2.2.5),is difficult to determine. Because the ACVP measures systematically lower k than the ADV,the discrepancies might be attributed to the lack of spatial temporal resolution of the ACVP,enhanced by the application of the Doppler noise correction method (Appendix A).
For the same reason, the ACVP measured Reynolds shear stress (Section 2.5.3) may alsounderestimate the actual fluid shear. It is not expected that this underestimation varies alongthe bed profile since the same ACVP settings were used throughout the experiment.Nevertheless, for this reason, a quantitative analysis of the different terms contributing to thetotal bed shear was not carried out. It should be noted that the Reynolds shear forms only onecomponent of the total bed shear. The time averaged and periodic velocities can alsocontribute to – and even dominate – bed shear in the surf zone (Chassagneux and Hurther,2014).
-ρ<u
'w'(δ
)> (N
/m2 )
-4
-2
0
2
4
crest
trough
Plunge point
(a)
x (m)50 55 60 65
z (m
)
-1.5
-1
-0.5(b)
0 min.90 min.
Near bed hydrodynamics under a plunging wave
61
The present results highlight an important contribution of breaking induced turbulence toTKE inside the wave boundary layer. This agrees with other large scale laboratory (Scott et al.,2005) and field (Grasso et al., 2012) studies over a barred profile that included measurementsof velocities within, or close to, the WBL. The WBL invasion of breaking generated turbulenceis most apparent at the bar crest and near the plunge point, where TKE increases after arrivalof a highly turbulent water body that follows rapidly (about 0.5 s) after the plunging jet strikesthe water column ( Figure 2.11, x = 55.5–56.0 m). This is consistent with previous studies thatshowed rapid downward turbulence transport under plunging breakers, associated with largevortices below the wave front (Ting and Kirby, 1995; Christensen and Deigaard, 2001;Kimmoun and Branger, 2007). It is expected that in the present study the rapid mixing of TKEover the complete water column including the WBL is partly facilitated by the shallow waterdepths at the bar crest. This suggests that the barred bed profile and cross shore varying waterdepth are important factors controlling the extent to which breaking induced TKE can reachthe WBL.
Breaking induced TKE is not fully determined by local vertical processes, i.e. production,dissipation and vertical advection and diffusion. Instead, breaking generated turbulencetravels offshore, leading to an increase in phase and time averaged TKE over the completewater column including the WBL up to about 3 m offshore from the plunge point. The phasedependency of the excursion suggests that transport of TKE is advective and links closely tothe orbital motion. The distance over which TKE is advected (3 m) equals approximately 6times the semi excursion length a and it corresponds to about 15 s (3 T) of advection byoffshore directed time averaged velocities. This suggests that offshore TKE advection occursover multiple wave cycles and that breaking generated TKE does not dissipate within onewave cycle. At the same time, previous research has shown that turbulence transport underplunging waves is not fully advective; diffusive transport may also be important (e.g. Tingand Kirby, 1995). A more detailed analysis of turbulence transport mechanisms is notconsidered here due to the relatively limited spatial coverage of outer flow velocitymeasurements. Results of an accompanying rigid bed experiment involving similar waveconditions and barred profile are expected to extend insights into the TKE transportmechanisms.
The increase in near bed Reynolds shear stresses in the breaking region agrees qualitativelywith previous observations of enhanced bed shear in the breaking region (Cox and Kobayashi,2000; Sumer et al., 2013) or under external grid turbulence (Fredsøe et al., 2003). Quantitativecomparisons between these previous studies are difficult, because of significant differences inscale, bed geometry, breaking intensity and instrumentation (i.e. the Reynolds stress in thepresent study differs physically from the total bed shear). It was shown by Fredsøe et al. (2003)that external turbulence may increase the apparent bed roughness and the WBL thickness.This raises the question to what extent the present study’s distinct increase in /a (factor 2 3compared to previous studies) in the breaking region ( Figure 2.9, from x=56.0 to 57.0 m) relatesto breaking induced turbulence or other factors. Three factors are discussed here.
Fredsøe et al. (2003) showed that external turbulence may enhance the turbulent exchange ofmomentum between free stream flow and the WBL, resulting in larger wave friction factorsover a wide range of Reynolds regimes (O(Re) = 104–106). This leads to an increase in apparentbed roughness and an upward displacement of periodic velocity in the inner WBL, similar to
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62
how wave induced mixing can affect steady current profiles (Fredsøe et al., 2003). In addition,the invasion of external turbulence leads to an earlier transition to turbulence in the WBL,which can increase /a with as much as a factor 2. Reynolds stresses (Figure 2.13) suggest asimilar enhanced momentum exchange between WBL and outer flow in the present study (x= 55.0 – 56.5 m) which is likely to affect velocity distributions inside the WBL. Whether thiseffect can explain the significant increase in /a cannot be concluded by quantitativecomparison with results by Fredsøe et al. (2003), because their results were obtained for asmooth bed which differs substantially from hydraulically rough conditions in terms ofturbulence intensities and Reynolds stresses at elevations close to the bed ( < ) (c.f. Jensen etal., 1989).
A second factor that may affect the WBL thickness is time averaged undertow velocity, that isparticularly strong (relative to periodic velocity) from x=56.5 to 58.0 m. Nielsen (1992), usingthe dataset of van Doorn (1981) that included values of relative current strength to rms periodicvelocity (| |/ rms) up to 1.11, found no effects of the superimposed current on WBL thickness.In the present study, locations from x = 56.5 to 58.0 m have | |/ rms values that exceed 1.11(Table 2.1). However, based on the results of Nielsen (1992) we deem that the superimposedcurrent cannot explain the strong (factor 3) enhancement of WBL thicknesses in the presentstudy. In addition, the enhanced WBL thickness is observed already at x=56.0 m, where theundertow strength is of moderate strength compared to periodic velocities (| |/ rms<1.11).
A third factor that potentially affects WBL thicknesses is the bed geometry. Sumer et al. (1993)showed that the WBL thickness for converging/diverging flow may differ substantially fromuniform flow conditions. In a tunnel with 0.20 m flow depth and with a local bed slope of 1°,the maximum WBL thickness during a diverging flow can be almost twice as thick as a WBLabove a uniform (zero inclination) bed (Sumer et al., 1993). In the present experiment, themaximum WBL thickness is estimated during the crest phase when the flow indeed diverges.One may expect that the importance of this effect depends on a relative vertical divergencerate during a wave cycle, i.e. the vertical expansion during the orbital motion relative to thelocal water depth. This can be expressed as a ratio a tan( )/h, in which a is the semi excursionamplitude, is the local slope, and h is the water depth (c.f. Fuhrmann et al., 2009a). In Sumeret al. (1993), this divergence ratio is approximately 0.26 (a=3.0 m). In the present experiment,along the lee side of the bar at x = 56.5 m, this ratio equals about 0.06 at the start of theexperiment (a=0.31 m, =11°, h=1.1 m; Table 2.1) and about 0.12 at the final stage of bardevelopment (as increases to 25°). Based on this, we may expect flow divergence effects inthe present study to be smaller but of same order of magnitude as the experiments of Sumeret al. (1993). Hence, effects of flow divergence on WBL thickness along the shoreward bar slopecannot be dismissed.
The high contributions of breaking induced turbulence to TKE in and just outside the WBLmay have important implications for sediment transport. Not only is turbulence able to entrainsediment from the bed into suspension (Sumer and Oguz, 1978), it has also the ability toincrease bedload transport (Sumer et al., 2003). The effects of breaking induced turbulence onsuspended and bedload sediment transport processes will be addressed in a forthcomingpaper.
Near bed hydrodynamics under a plunging wave
63
2.7 Conclusions
The present study examines velocities and turbulence dynamics near a sand bed under nearfull scale, plunging breaking waves in a laboratory wave flume. In contrast with previousexperiments, detailed measurements were obtained inside and directly above the wavebottom boundary layer (WBL) with high spatial and temporal resolution. These measurementswere taken along a mobile sandy breaker bar at shoaling, breaking and inner surf zonelocations. The following conclusions are made:
1. Phase averaged WBL velocities show similar behavior to non breaking and oscillatoryWBL studies, including distinct velocity overshooting. Time averaged velocities in theWBL are largely dominated by the strong undertow and show consistent behavior withprevious observations for wave current interactions. Wave (shape) streamingmechanisms, as usually observed for uniform non breaking waves, are evident only inthe shoaling region where the undertow is relatively weak.
2. The dimensionless WBL thickness along the offshore slope of the breaker bar agreeswith previous mobile bed oscillatory flow studies, suggesting that wave nonuniformity does not affect the WBL thickness. However, near the breaking waveplunge point and along the shoreward slope of the bar, /a is about 3 times higher thanpredictions based on uniform oscillatory flows. This can be attributed to the combinedeffects of breaking induced turbulent kinetic energy (TKE) and flow divergenceinduced by the bed geometry.
3. Outer flow TKE observations match with previous breaking wave studies, showinghighest values in the breaking region at the breaker bar crest, followed by a decreasein the bar trough. In close vicinity of the plunge point (+/ 0.5 m), TKE is almost depthuniform over the complete water column (including the WBL), indicating largeturbulence production and a strong penetration into the water column down to thebed. At shoaling and inner surf zone, vertical profiles of TKE show that also bedfriction is a significant source of near bed turbulence.
4. Near the plunge point, TKE enters the boundary layer during two instances of the wavecycle: a first occurrence rapidly (about 0.5 s) after wave plunging, when breakinginduced TKE rapidly saturates the complete water column including the WBL; asecond occurrence during the wave trough phase, when undertow and periodicvelocities transport TKE towards the breaker bar. This invasion results in an increasein maximum TKE inside the WBL with a factor of almost three between shoaling andbreaking region, despite decreasing near bed velocity magnitudes.
5. Breaking generated turbulence travels horizontally offshore (during trough phase)and back onshore (during crest phase) between breaking and shoaling zone, leading toincreased phase and time averaged TKE over the near bed region (including theWBL). Hence, the area affected by breaking generated turbulence is not restricted tothe breaking region itself, but extends to shoaling locations about 3 m offshore fromthe plunge point. Advection of TKE from plunge point in onshore direction is restrictedby the combination of a decreased orbital velocity amplitude and strong offshoredirected undertow velocities.
6. Wave breaking affects near bed Reynolds shear stresses, leading to an increase inmaximum onshore and offshore phase averaged Reynolds stresses at the WBL
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64
overshoot elevation. The effect is mostly apparent for the region comprising +/ 1 maround the plunge point, where phase averaged Reynolds stress magnitudes are afactor 2 higher than at shoaling locations at the bar crest.
2.A. Additional information on ACVP measurements and data treatment
Additional data treatment was required for ACVP measured turbulence. An examplespectrum of ACVP measured horizontal velocities is shown in Figure 2.A1. A contribution ofDoppler noise appears as a deviation from the 5/3 slope that is expected at inertial subrangefrequencies. In the present measurement conditions, this Doppler noise is caused by a lack ofsuspended particles as acoustic targets. Noise contributions are higher at shoaling than surfzone locations, as more sediment grains are entrained in the breaking and inner surf zoneregions.
Figure 2.A1. Spectra of horizontal velocity measurements by ACVP at edge of boundary layer ( = ),shoaling region. Figure includes auto spectrum of raw data (thin black line), auto spectrum of
decomposed turbulent signal after applying de spiking through moving median (grey line), and crossspectrum of turbulent velocities at = z and = + z, equivalent to Equation 2.7 (thick black line).
A two step correction was applied to reduce the Doppler noise contribution. Firstly, data werede spiked by applying a moving median with a window width of 5 samples. Figure 2.A1shows that this step importantly reduces energy at frequencies contaminated with Dopplernoise (f > 5 Hz). Secondly, phase averaged turbulent intensities were calculated using a twopoint cross correlation method as proposed by Garbini et al. (1982):
<urms z,t >= <u z z,t u (z + z,t)> (2.7).
This method is based on the assumption that the most energetic turbulent eddies are largerthan the separation distance 2 z, with z equal to the ACVP’s vertical resolution (1.5 mm).
f (Hz)10-2 10-1 100 101 102
PSD
(m2 /s
)
10-6
10-4
10-2
100
f -5/3
RawDe-spikedNoise-corrected
Near bed hydrodynamics under a plunging wave
65
Consequently, the uncorrelated velocity fluctuations constituted mainly by Doppler noise donot contribute to the turbulence co variance given by Equation 2.7. This method waspreviously applied successfully in Hurther and Lemmin (2001, 2008) in shear and purelydiffusive turbulent flows to supress the Doppler noise contribution in the normal Reynoldsstress and TKE profile measurements. Figure 2.A1 shows that the applied cleaningmethodology effectively removes Doppler noise, as the cleaned turbulent velocity spectrumfollows the expected 5/3 slope in the inertial subranges. Although Doppler noise was largelyrestricted to the horizontal velocity measurements (due to the strong geometrical weighting,c.f. Hurther and Lemmin, 2001), Equation 2.7 was also applied to the vertical turbulentvelocities w’rms for consistency.
In terms of noise effects on Reynolds stresses, previous research found that Doppler noise isintrinsically uncorrelated in the horizontal and vertical directions (Hurther and Lemmin,2001). However, this is only true if the transmission direction of the ACVP is normal to thelocal bed slope. As this is not the case in the present experiment, Equation 2.7 is similarlyapplied to the Reynolds shear stress using a centered scheme version:
–<u’w’(z, t)> = –0.5[<u’(z – z, t) w’(z + z, t)> + <u’(z + z, t) w’(z z, t)>] (2.8).
The Reynolds shear may be affected by contributions of wave velocities that are still presentin u’ and w’ after the Reynolds decomposition (see Section 2.2.5). Feddersen and Williams(2007) proposed testing of wave bias effects on u’w’ using the cumulative distribution of thecross spectrum of u’ and w’ (ogive curves). Wave bias appears in the ogive curves as a localincrease in curve steepness around frequencies associated with the waves. The curves werecalculated following the mathematical expression by Feddersen and Williams (2007) for eachindividual run. Following previous studies in field (Feddersen and Williams, 2007; Ruessink,2010) and laboratory (Brinkkemper et al., 2015) surf zones, the Reynolds stresses were removedfrom the analysis if the ogive curves exceeded limits of 0.5 and +1.6 at any frequency or whenvisual inspection of the curves revealed a dominance of wave contributions to Reynolds shear.In total, 9 out of 72 runs failed the ogive test and were excluded. The exclusion of these runsdid not significantly alter the results.
In order to interpret the ACVP data properly, a few considerations regarding the estimates ofturbulence quantities from the ACVP measurements are addressed. First, the ACVP measuresvelocities of sand grains as the dominant source of acoustic scattering. Depending on the localhydrodynamic conditions, the particle velocity may lag the fluid velocity due to particle inertiaeffects. Consequently, the near bed turbulence data provided by the ACVP might differ frompure fluid turbulence data. Unfortunately, to our knowledge, this measurement limitationcannot be overcome presently in the absence of instrumentation capable of measuring fluidvelocity data under such dense water sediment mixtures. Second, application of Equation 2.7also eliminates the fraction of TKE contained in eddies smaller than the separation distance2 z. However, while the noise correction reduces spectral energy at inertial subrangefrequencies (f > 1 Hz), the energy associated with the larger energy containing vortices thatcontribute most to TKE (f 0.25 to 1.0 Hz) is hardly affected (Figure 2.A1). Third, inside theWBL, the size of eddies reduces significantly within proximity of the bed. These small scaleturbulent eddies may not be properly resolved by the ACVP due to a lack of spatial temporalresolution (Soulsby, 1980). This may lead to an underestimation of turbulence intensities;
Chapter 2
66
especially for the vertical turbulent fluctuations w’, which in the vicinity of the bed exhibitmuch smaller turbulent scales than u’ (Soulsby, 1980). At the same time, near bed TKE isdominated by strongly anisotropic eddies with u’rms much larger than w’rms (Cox andKobayashi, 2000). As a result, TKE is not severely underestimated by the ACVP. In order toquantify the underestimation, a comparison was carried out between the ACVP and a twocomponent LDA system (with a roughly 4 times higher spatial temporal resolution),simultaneously deployed in an equivalent clear water wave experiment over a rigid bed. TheACVP measurements showed an underestimation in k/umax of 10 to 15% at a distance = 8mm above the rigid bed (corresponding to about half the WBL thickness). The spatialaveraging effect on Reynolds stress measurements is supposedly limited due to the muchlarger size of shear producing eddies – typically of the order of the WBL thickness (Soulsby,1980).
Near bed hydrodynamics under a plunging wave
67
Chapter 3
68
3 Suspended sediment transportaround a large scale laboratorybreaker bar
Highlights:
Near bed reference concentrations correlate significantly with near bed turbulentkinetic energy.
Depth integrated suspended transport is dominated by offshore directed currentrelated fluxes at outer flow elevations; the onshore wave related transport is generallyconfined to the wave bottom boundary layer.
The contributions of horizontal sediment advection and of vertical exchange with thebedload layer (pick up/deposition) are quantified to explain the complex intra wavespatiotemporal behavior of near bed suspended sediment concentrations.
Suspended sediment under a breaking wave
69
Abstract
This paper presents novel insights into suspended sediment concentrations and fluxes undera large scale laboratory plunging wave. Measurements of sediment concentrations andvelocities were taken at 12 locations around an evolving breaker bar, covering the completebreaking region from shoaling to inner surf zone, with particular high resolution near the bedusing an Acoustic Concentration and Velocity Profiler. Wave breaking evidently affectssediment pick up rates, which increase by an order of magnitude from shoaling to breakingzone. Time averaged reference concentrations correlate poorly with periodic and timeaveraged near bed velocities, but correlate significantly with near bed time averagedturbulent kinetic energy. The net depth integrated suspended transport is offshore directedand primarily attributed to current related fluxes (undertow) at outer flow elevations (i.e.above the wave bottom boundary layer). The wave related suspended transport is onshoredirected and is generally confined to the wave bottom boundary layer. Cross shore gradientsof sediment fluxes are quantified to explain spatial patterns of sediment pick up anddeposition and of cross shore sediment advection. Suspended particles travel back and forthbetween the breaking and shoaling zones following the orbital motion, leading to local intrawave concentration changes. At locations between the breaker bar crest and bar trough, intrawave concentration changes are due to a combination of horizontal advection and of verticalexchange with the bedload layer: sediment is entrained in the bar trough during the wavetrough phase, almost instantly advected offshore, and deposited near the bar crest during thewave crest phase. Finally, these results are used to suggest improvements for engineering typesuspended transport models.
______________________________________________________________________________
This chapter is under review for publication in Coastal Engineering as:
van der Zanden, J. van der A, D. A., Hurther, D., Cáceres, I., O’Donoghue,T. and J.S. Ribberink.Suspended sediment transport around a large scale laboratory breaker bar.
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3.1 Introduction
Over the last decades, experimental and numerical studies have significantly advanced theunderstanding of sediment transport processes and the ability to predict suspended andbedload transport rates for non breaking waves (Van Rijn et al., 2013). However, in thebreaking region, existing formulations for suspended sediment concentrations and transportmay not be valid due to effects of breaking generated turbulence and of cross shorehydrodynamic non uniformity (i.e. cross shore changes in wave shape and undertow) whichare not fully understood (Van Rijn et al., 2013).
Laboratory (Steetzel, 1993; Roelvink and Reniers, 1995; van Thiel de Vries et al., 2008) and fieldstudies (Nielsen, 1984; Yu et al., 1993; Beach and Sternberg, 1996) have reported large amountsof suspended sediment in the breaking zone, related to the enhancing effects of breakinggenerated vortices on sediment entrainment from the bed (Nielsen, 1984; Nadaoka et al., 1988;van Thiel de Vries et al., 2008; Scott et al., 2009; Aagaard and Hughes, 2010; Sumer et al., 2013)and on vertical sediment mixing (Nielsen, 1984; Ogston and Sternberg, 2002; Aagaard andJensen, 2013; Yoon et al., 2015). These processes depend on the characteristics of the breakingwave, with plunging breakers being more effective in entraining and mixing sediment thanspilling breakers (Nielsen, 1984; Aagaard and Jensen, 2013). This relates to differences inturbulence behavior, with higher production rates and a more rapid downward spreading ofbreaking induced turbulence found under plunging than under spilling waves (Ting andKirby, 1994).
Due to the dominance of breaking induced vortices on sediment pick up, existingformulations for near bed reference concentrations that are based on orbital and timeaveraged velocities (Nielsen, 1986; Van Rijn, 2007b) may not apply in the wave breaking region(Aagaard and Jensen, 2013). Instead, formulations that are based on breaking inducedturbulence and that take the breaker type into account (e.g. Mocke and Smith, 1992; Steetzel,1993; Kobayashi and Johnson, 2001) appear more appropriate. An additional complication isthat due to strong horizontal sediment advection in the breaking region (Scott et al., 2009; Yoonand Cox, 2012) the near bed concentrations may not always be related to local hydrodynamicsonly.
The net horizontal suspended flux in the breaking region is the result of two opposing fluxeswith similar magnitudes: an offshore directed current related flux and an onshore directedwave related flux (Osborne and Greenwood, 1992; Ogston and Sternberg, 1995; Thornton etal., 1996; Ruessink et al., 1998). The former is driven by the undertow, whereas the latter relatesto the wave asymmetry (Elgar et al., 2001; Hoefel and Elgar, 2003). Time varying breakinggenerated turbulence, with higher intensities during the crest half cycle, has been suggestedas an additional factor contributing to onshore wave related suspended sediment fluxes (Tingand Kirby, 1994; Boers, 2005). Yoon and Cox (2012) presented experimental evidence forincreased onshore wave related suspension fluxes due to intermittent suspension events thatoccur preferentially during the wave crest phase following events of high turbulent energy.However, Scott et al. (2009) found, by combining data from the same experiment withnumerical simulations, that suspension events occur mainly during the wave trough phaseand contribute to offshore directed fluxes. The individual effects by turbulence and wave
Suspended sediment under a breaking wave
71
asymmetry on sediment fluxes are difficult to assess because the two parameters correlatepositively in the breaking region (van Thiel de Vries et al., 2008; Aagaard and Hughes, 2010).
Although previous research highlighted clear effects of wave breaking on sedimentsuspension and fluxes, there are still open research questions. Most of the aforementionedstudies are based on local point measurements of sediment concentrations at few elevations inthe water column, sometimes combined with co located velocity measurements to estimatethe local sediment fluxes. These measurements did not capture the complete verticaldistribution of fluxes since the near bed region including the wave bottom boundary layer(WBL), where large contributions to total suspended transport can be expected, was notaccurately resolved. Such measurements of WBL flow and time varying near bed turbulenceare also essential in relating the observed sediment processes to hydrodynamic forcing. Inaddition, most of the previous experimental studies covered only a few cross shore locationsin the shoaling and breaking region. This strongly limits the study of cross shore advection ofsuspended sediment and the effects of cross shore non uniformity in hydrodynamics (i.e. flowand turbulence) on suspended sediment processes.
Here we present new high resolution measurements of suspended sediment transportprocesses under a plunging wave in a large scale wave flume. Measurements were obtainedat 12 cross shore locations along a sandy breaker bar, covering the complete breaking regionfrom shoaling zone to inner surf zone. Sediment concentration and velocity measurementscover most of the water column, with particular high resolution of time varyingconcentrations and sediment fluxes in the near bed region (including the WBL). The aim is toimprove insights into suspended sediment processes in the breaking region, with particularfocus on the current related, wave related and turbulent suspended sediment fluxcomponents and their contributions to the total net suspended transport. These fluxes are alsoused to explain the intra wave near bed concentration field in terms of horizontal sedimentadvection and vertical exchange of sediment between the suspension and bedload layer (pickup and deposition). Results of the sediment dynamics are related to the detailed near bed flowand turbulence measurements obtained from the same experiment and reported in Chapter 2.
The paper is organized as follows: the experiment is described in Section 3.2. Section 3.3presents the bed profile evolution and the cross shore variation in the main hydrodynamicparameters. Section 3.4 presents results on suspended sediment concentrations (3.4.1), fluxesand net transport rates (3.4.2) and horizontal advection and pick up/deposition (3.4.3). Theresults are used to discuss potential improvements to engineering type suspended sedimenttransport formulations for breaking wave conditions (Section 3.5).
3.2 Experimental description
3.2.1 Facility and test conditions
The experiments were carried out in the large scale CIEM wave flume at the UniversitatPolitècnica de Catalunya (UPC) in Barcelona. The flume is 100 m long, 3 m wide and 4.5 mdeep, and is equipped with a wedge type wave paddle. Figure 3.1 shows the experimental setup and bed profile for the present study. Cross shore coordinate x is defined positivelytowards the beach, with x = 0 at the toe of the wave paddle. Vertical coordinate z is defined
Chapter 3
72
positively upwards with z = 0 at the still water level (SWL); is the vertical coordinate positiveupwards from the local bed level.
The initial bed profile consisted of a bar trough configuration (Figure 3.1a, black line) that wasproduced by 105 minutes of wave action over an initially flat horizontal test section (seeChapter 2). The test section can be roughly divided into an offshore facing slope of the breakerbar (x = 35.0 to 54.8 m; steepness tan( ) = 1:10), followed by a steeper shoreward facing barslope (x = 54.8 to 57.5 m; –tan( ) = 1:4.7), and a mildly sloping bed shoreward from the bartrough (x = 57.5 to 68.0 m; tan( ) = 1:95). The test section consisted of medium sand (mediandiameter D50 = 0.24 mm), which had a measured settling velocity ws = 0.034 m/s. The profileshoreward of the mobile test section (x > 68.0 m) followed a 1:7.5 slope, and was fixed withgeotextile and covered with perforated concrete slabs that promoted wave energy dissipation.
Figure 3.1. Experimental set up and measurement locations. (a) Initial bed profile (black line) andfixed beach (grey line), and locations of resistive wave gauges (RWGs, vertical black lines); (b)
Measurement positions of ADVs (star symbols), mobile frame Pressure Transducers (PT, whitesquares), wall deployed PTs (black squares), Transverse Suction System nozzles (TSS, black dots),
Optical Backscatter Sensor (black crosses), and measuring range of mobile frame ACVP (grey boxes).
The experiments involved monochromatic waves with wave period T = 4 s and wave heightH0 = 0.85 m at water depth h0 = 2.55 m near the wave paddle. These conditions correspond toa surf similarity parameter 0 = 0.54 (where 0= tan ( )/ H0/L0, tan( ) is the offshore bar slopeand L0 is the deep water wave length), which, in agreement with the classification of Battjes(1974), resulted in a plunging type breaker.
Based on measurements and visual observations of the water surface and following theterminology of Smith and Kraus (1991), we define the break point (x = 53.0 m) as the location
0 10 20 30 40 50 60 70 80
z (m
)
-2
-1
0 SWL
RWGs
h0=2.55 mht=1.35 m
x
H=0.85 m, T=4 s(a)
x (m)50 55 60 65
z (m
)
-1.5
-1
-0.5
0
0.5(outer) breaking regionshoaling region inner surf zone
ACVP
ADV
PT (mob.)
TSS
PT (wall)
ζ
zSWL break point plunge point splash point
(b)
Suspended sediment under a breaking wave
73
where the breaking wave starts to overturn, the plunge point (x = 55.5 m) where the plungingjet hits the water surface, and the splash point (x = 59.0 m) where the pushed up water strikesthe water surface a second time and where the breaking wave has transformed into a surf bore.Following Svendsen et al. (1978) we define the shoaling zone as the region up to the plungepoint (x < 55.5 m), the breaking zone as the region between plunge and splash point (55.5 < x< 59.0 m), and the inner surf zone as the region shoreward from the splash point (x > 59.0 m).
3.2.2 Instrumentation
Most instruments were deployed from a custom built mobile frame (Figure 3.2). This frameconsisted of stainless steel tubing with 30 mm diameter and was designed such that it wouldhave minimum flow perturbation while being sufficiently stiff to withstand wave impact. Theframe was mounted to a horizontally mobile trolley on top of the flume, and could bepositioned with sub mm accuracy in the vertical direction using a spindle (for more details,see Ribberink et al., 2014). The mobile frame set up enabled measurements at various crossshore positions, while maintaining an approximately equal elevation of the instrumental arraywith respect to the bed at the start of each run. The positions of the various instruments abovethe initial bed level are presented in Table 3.1.
Figure 3.2. Mobile measuring frame and instrumentation. Instrumentation includes three ADVs (bluesolid circles), one Pressure Transducer (yellow square), a six nozzle Transverse Suction System
(yellow circles), an OBS (black dashed circle) and an ACVP (blue square). Inset shows close up ofnear bed instrumentation.
Chapter 3
74
Outer flow velocities were measured with a vertical array of three three component (crossshore, lateral, and vertical; annotated u, v, and w, respectively) Acoustic Doppler Velocimeters(ADVs; Figure 3.2). The ADVs operated at an acoustic frequency of 10 MHz and had asampling volume of approximately 3 mm radius.
Near bed flow and sediment concentrations were measured with a High Resolution AcousticConcentration and Velocity Profiler (ACVP) that is fully described in Hurther et al. (2011). TheACVP measures simultaneous and co located vertical profiles of 2 component (u, w) particlevelocity and sediment concentration. Operating at an acoustic frequency of 1 MHz, i.e.considerably lower than the frequency of commercial ADV technology, the ACVP isparticularly suitable for measuring velocities and sediment concentrations across a dense nearbed sediment layer, as demonstrated in recent mobile bed studies with steady (Naqshband etal., 2014; Revil Baudard et al., 2015) and wave driven (Chassagneux and Hurther, 2014) flows.In the present experiment, the ACVP’s acoustic and geometrical settings were set to measurevelocities up to 1.8 m/s over a 20 cm near bed profile, with a vertical sampling bin resolutionof 1.5 mm and a sampling frequency of 70 Hz. Since the bed is contained within the measuringvolume and changes during a run, the effective profiling length above the bed was in the rangeof 10 to 15 cm. Section 3.2.3 explains the inversion of the measured acoustic intensities tosediment concentrations.
Table 3.1: Elevations of mobile frame instrumentation with respect to initial bed level.
Instrument Elevation (m)Acoustic Doppler Velocimeters (ADVs) 0.11, 0.38, 0.85
High Resolution Acoustic Concentration andVelocity Profiler (ACVP)
0.12 (elevation transmitter)
Transverse Suction System (TSS) nozzles 0.02, 0.04, 0.10, 0.18, 0.31, 0.53Optical Backscatter Sensor (OBS) 0.07
Pressure Transducer (PT) 0.48
Time averaged sediment concentrations were obtained with a six nozzle Transverse SuctionSystem (TSS), consisting of six stainless steel nozzles, each connected through plastic tubingto a peristaltic pump on top of the wave flume. Following Bosman et al. (1987), the TSS wasdesigned to have intake velocities of 2.3 m/s, i.e. exceeding the maximum orbital velocity byapproximately 1.5, in order to guarantee a constant sediment trapping efficiency. The nozzleintake diameter was 3 mm (same as Bosman et al., 1987) and the pump discharge was 1 L/min.The 30 mm long nozzles were oriented parallel to the bed and perpendicular to the wavedirection (Figure 3.2).
The TSS tubing consisted of 2 m long, 4 mm diameter rigid air hose tubing at the lower partof the frame, and 4 m long, 8 mm diameter silicone tubing at higher levels. The estimatedwater velocity in the widest suction hose was 0.3 m/s, which exceeds the sediment settlingvelocity by an order of magnitude. The sampled water plus sediment mixture was capturedin 15 L buckets, which were weighted (to measure the water content), carefully drained toremove excess water, transferred to aluminum cups, and then dry weighted to give a firstmeasure of the concentration Cs. The actual concentration Ctrue is then obtained from Ctrue = tCs,
Suspended sediment under a breaking wave
75
where the factor t = 1 + 1/3arctan(D50/0.09) is the inverse of the nozzle’s trapping efficiency(Bosman et al., 1987). The estimated TSS measuring error is 10% and includes errors in thevarious processing steps (estimation of trapping efficiency, transfer of samples, water volumeestimation, dry weighting) and also uncertainties in the time varying elevation with respectto the bed (Bosman et al., 1987).
Additional time varying concentration measurements were obtained at 40 Hz using an OpticalBackscatter Sensor (OBS), which was located close to the bed and within the ACVP measuringrange (Figure 3.2). The OBS was calibrated at UPC through experiments with a replica of theapparatus described by Downing and Beach (1989) using samples of the sand in the flume.The OBS data were used for validating the phase averaged calibrated ACVP concentrations.
Water surface levels were sampled at 40 Hz, using pressure transducers (PTs) and resistive(wire) wave gauges (RWGs) that were deployed from the side walls of the flume (Figure 3.1)and an additional PT on the mobile frame (Figure 3.2). PT measurements of the dynamicpressure were converted to water surface levels using linear wave theory (following Guza andThornton, 1980). This conversion could be applied up to a frequency of 0.33 Hz, which in thepresent study includes the primary wave frequency (0.25 Hz) but not the higher harmonics.The actual wave height is therefore underestimated by approximately 10%.
Using echo sounders deployed from a second mobile trolley, bed profile measurements wereobtained at 2 cm cross shore resolution along two transects at lateral distances of 0.1 and 0.7m with respect to the flume’s centerline. The echo sounders had an estimated accuracy of +/–1 cm. The measured bed profile was taken as the mean of the profiles measured by the twosensors.
3.2.3 Measurement procedure
One experiment consisted of 90 minutes of waves, consisting of six individual 15 minute runs,during which the bed profile evolved. The bed profile was measured prior to the first run andafter every 2nd run, i.e. at t = 0, 30, 60 and 90 min. After the sixth run, the flume was drained.The initial bed profile, drawn as template on the side walls, was then restored by shovelingback transported sand and flattening any bed forms that were generated. The 90 minuteexperiment was repeated 12 times, with the mobile measuring frame moved to a new crossshore location for each experiment, which resulted in a high spatial coverage of measurements(Figure 3.1b). The measurement locations cover 0.9L, where L is the measured wave length inthe test section, and comprise the shoaling to inner surf zone. The high repeatability of thehydrodynamics and bed profile evolution following this procedure was demonstrated inChapter 2.
3.2.4 Data treatment
For each 15 minute run the first 5 minutes of data were discarded because the breakinglocation varied with time since no hydrodynamic equilibrium was established yet. Thebreaking point stabilized after the 5 minute period, leaving 10 minutes of data for analysis.Flume seiching induced a standing wave with an amplitude of O(cm) and a 45 s period. This
Chapter 3
76
long wave was removed from all water surface and velocity data by applying a high pass filterwith a cut off frequency of half the primary wave frequency (0.125 Hz). The auto spectra andautocorrelation functions of suspended sediment concentrations (OBS, ACVP) and timevarying bed levels (ACVP) did not reveal any distinct peaks at the seiching wave frequency.This shows that flume seiching had a negligible effect on sediment transport.
ADV and ACVP velocity data were de noised as explained in Chapter 2. The instantaneousbed level was obtained from the ACVP using the acoustic bed interface tracking methodproposed by Hurther and Thorne (2011). The bed level was used to correct the ACVP data forlocal bed evolution by assigning a level to each vertical measurement bin for each wave, with= 0 corresponding to the measured bed level during the zero down crossing of the water
surface when the bed is considered to be at rest. The ACVP data were then ensemble averagedfor each bin class. Following this procedure, bed level changes at intra wave time scale arestill considered in the ensemble means. Horizontal and vertical velocity u and w were rotatedto bed parallel uR and bed normal wR components, calculated using
uR = u cos( ) + w sin( )
wR = w cos( ) u sin( ) (3.1)
where is the rotation angle that minimized the orbital velocity amplitude of wR close to thebed (at = 0.03 m). Equation 3.1 was applied per individual wave cycle, i.e. was determinedfor each individual wave. The mean rotation angle for each run was found to match closelythe local bed slope obtained from the bed profile measurements, which supports the validityof the rotation procedure.
The inversion of the ACVP’s backscattered acoustic intensity to give sediment concentrationsfollowed the iterative implicit inversion method described by Hurther et al. (2011). Sedimentconcentrations C(ž) at distance ž from the transmitter were calculated iteratively, by movingfrom the transmitter downwards while accounting for attenuation of the backscattered signalalong the travel path of the acoustic beam:
C(ž) ž) for ž = 0
C(ž+ ž) = C(ž) J(ž+ ž) exp( sC(ž) r) for ž + ž > 0. (3.2),
where s is a sediment attenuation constant that depends on theoretical and empirical sedimentproperties; r is the change in distance with respect to the acoustic receivers that correspondswith a vertical displacement ž; and J(ž) is the normalized back scattered voltage calculatedusing
J(ž) =I(ž)Ah,s(ž)
(3.3)
where I(ž) is the backscatter voltage and Ah,s(ž) is a depth varying function that depends onhardware characteristics, water absorption effects and sediment characteristics. For thepresent experiments, both Ah,s(ž) and s are used as calibration parameters, with the formervarying with cross shore location and the latter a constant value for all experimental runs. Thecalibration was effected by matching the time averaged ACVP concentrations with the TSS
Suspended sediment under a breaking wave
77
measurements. Before the inversion, the acoustic backscattered voltage was de spiked using amoving median filter with a window width of 5 measurements.
Data were phase averaged over a wave cycle using the zero crossings of the RWG measuredwater surface elevation at x = 47.6 m as a phase reference. The number of wave cycles for phaseaveraging was about 150 for water surface and outer flow velocity data, but somewhat lower(typically about 100, with a minimum of 40) for the ACVP data. ACVP measurements werediscarded when the local bed eroded beyond the ACVP measuring volume or when it accretedto within 5 cm of the ACVP transmitter. In the inner surf zone, where bed forms migratedslowly offshore below the ACVP, intervals of time series used for phase averaging werechosen such that exactly 1 or 2 complete bed forms were captured (i.e. the data presented hereare ripple averaged). Phase averaged quantities are annotated with angle brackets and arenormalized such that t/T = 0 corresponds to maximum water surface level (wave crest) at x =50.0 m. Velocities were decomposed into time averaged (u w), periodic (u, w) and turbulent(u’, w’) components. Subscript rms is used to denote root mean square magnitudes of periodicvelocities. Additional information on the applied data cleaning procedures and the method toestimate turbulent kinetic energy k can be found in Chapter 2.
3.3 Bed evolution and hydrodynamics
This section discusses the bed profile evolution and the cross shore variation in hydrodynamicparameters. A more extensive description of the measured near bed hydrodynamics,including turbulence, can be found in Chapter 2.
The profile development in Figure 3.3a shows that the bar crest grows and migrates slightlyonshore during the experiment. This leads to an increase in the bar’s offshore slope fromtan( )=0.10 to tan( )=0.13 and an increase in the surf similarity parameter 0 from 0.54 to 0.68.At the same time the bar trough deepens, resulting in a steepening of the shoreward facingslope of the bar from tan( ) = –0.21 to tan( ) = –0.48. At 90 minutes, the slope approaches thenatural angle of repose ( = 26–34°) for sandy materials (Nielsen, 1992).
Bed forms were observed after draining the flume. The bed was flat in the shoaling regionuntil the bar crest (x = 48.0 to 55.5 m). Quasi 2D features (quasi uniform in longshore direction)were identified along the shoreward facing slope of the bar (x = 55.5 to 57.0 m), where theymigrated progressively offshore. Shoreward facing lunate shaped features were present at thebar trough (x = 57.0 to 59.0 m). In the inner surf zone, a gradual transition to quasi 2D bedfeatures occurred (from x = 59.0 to 62.0 m). Further shoreward these features becameincreasingly irregular while their wave length reduced, resulting in 3D sand ripples (x = 62.0m to 68.0 m). Only in the inner surf zone (x 59.0 m), bed form lengths were of similarmagnitude as the orbital semi excursion length a (Table 3.2).
Figure 3.3a shows that wave height decreases by 50% between the break point (x = 53.0 m) andsplash point (x = 59.0 m). Time averaged water levels show set down in the shoaling zoneand set up in the inner surf zone. Figure 3.3b shows the maximum offshore and onshorephase averaged velocities in bed parallel direction at = , where ( 0.01 to 0.02 m) is theWBL overshoot elevation during the crest phase. The reduced wave height and the increasingwater depth shoreward of the bar crest (x = 55.0 to 57.0 m) leads to a strong decrease in
Chapter 3
78
amplitudes of periodic velocities while the offshore directed time averaged velocity(undertow) increases in magnitude. Consequently, along the shoreward facing slope of thebar (x = 56.0 to 57.5 m) the near bed velocities are directed offshore during (almost) the entirewave cycle.
Figure 3.3. (a) Bed profile evolution (solid lines, with each line representing the mean value over allexperimental days), and water levels for t=0–15 min. (dots and dashed lines depict time averaged andenvelope, respectively); (b) ACVP measured bed parallel velocities at the WBL overshoot elevation,uR( ), for t=0–15 min., mean (circles) and maximum onshore and offshore values (dots and dashed
line); (c) Turbulent kinetic energy, mean values over experiment (t=0–90 min.) at outer flow elevation= 0.38 m (measured with ADV, solid line and circles) and maximum time averaged TKE inside the
WBL (measured with ACVP, dashed line and squares).
Figure 3.3c shows the time averaged turbulent kinetic energy (k) at outer flow elevation =0.38 m and inside the WBL (kb). The latter is defined as the maximum k at . Turbulenceproduction by wave breaking leads to large magnitudes of outer flow k in the vicinity of theplunge point at x = 55.5 m. At most locations, k decreases towards the bed, indicating that atouter flow elevations the dominant source of turbulence is production near the water surfacedue to wave breaking. Breaking generated turbulence is advected to offshore locations whilegradually dissipating, leading to a decrease in TKE from the breaking zone in the offshoredirection (from x = 55.5 to 51.0 m). TKE inside the WBL (kb) increases by an order of magnitudefrom the shoaling zone (x = 51.0 m) to the breaking region (x = 53.0 to 58.0 m). This increaseoccurs in spite of a reduction in peak onshore/offshore velocities, which shows that the
z (m
)
-1.5
-1
-0.5
0
0.5
SWL
ηcrest
η
ηtrough
(a)
plunge pointbreak point splash point
t=0 min.t=30 min.t=60 min.t=90 min.
u R(δ
) (m
/s)
-1-0.5
00.5
1uR,crest
uRuR,trough
(b)
x (m)50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
k (m
2 /s2 )
0
0.01
0.02
0.03(c)
k(ζ = 0.38 m)kb
Suspended sediment under a breaking wave
79
increase is not due to turbulence production by bed shear, but instead is due to the invasionof breaking generated TKE into the WBL. The increase in kb throughout the inner surf zone (x
59.0 m) is due an increase in bed roughness (i.e. due to bed forms) and in turbulenceproduction at the bed.
Table 3.2: Hydrodynamic parameters at all measurement locations (t=0–15 min.): water depth (h);wave height (H); time averaged bed parallel velocity ( R); maximum (crest phase) and minimum(trough phase) phase averaged bed parallel velocities; semi excursion length (a = 2T rms/2 ).
Velocities are based on measurements from the lowest ADV at =0.11 m.
x(m)
h(m)
H(m)
R
(m/s)<uR>max(m/s)
<uR>min(m/s)
a(m)
51.0 1.10 0.79 0.13 1.04 0.83 0.5453.0 0.97 0.74 0.22 0.80 0.94 0.4854.5 0.88 0.64 0.19 0.84 0.85 0.4755.0 0.88 0.60 0.24 0.78 0.90 0.4755.5 0.97 0.51 0.23 0.57 0.83 0.3956.0 1.10 0.50 0.30 0.25 0.82 0.3156.5 1.19 0.53 0.51 0.05 0.83 0.2557.0 1.24 0.48 0.54 0.02 0.78 0.2358.0 1.28 0.47 0.46 0.01 0.71 0.2159.0 1.28 0.43 0.36 0.13 0.71 0.2360.0 1.26 0.42 0.36 0.17 0.66 0.2463.0 1.26 0.41 0.34 0.19 0.58 0.23
3.4 Suspended sediment transport processes
Several definitions for bedload and suspended load can be found in the literature. From aphysical perspective, bedload can be defined as the transport that is supported byintergranular forces and the suspended load as transport supported by fluid drag (Bagnold,1956). Others, following a more pragmatic approach, have defined bedload (suspended load)as the transport below (above) a reference elevation, i.e. the level of the bed (Nielsen, 1986) ora roughness dependent elevation slightly above the bed (Van Rijn, 2007a; Van Rijn, 2007b). Inthe present study, we use a wave averaged reference elevation at = 0.005 m to distinguishbetween bedload ( < 0.005 m) and suspended load ( > 0.005 m). This is based firstly onphysical arguments, as bedload in the present experiment occurs partly in the sheet flowregime and sheet flow transport is usually considered part of bedload (Ribberink, 1998). In thepresent study, detailed sheet flow layer measurements were obtained near the bar crest wherethe top of the sheet flow layer was found at 0.005 m (Chapter 4). Secondly, although theACVP is capable of measuring sediment fluxes in the upper part of the bedload layer(Naqshband et al., 2014), the bedload fluxes derived from the ACVP were in the present studyvery sensitive to the acoustic inversion parameter due to the very high vertical gradient ofsediment concentrations in the sheet flow layer. For these two reasons, which potentially resultin large errors of estimated depth integrated transport inside the WBL, it was decided totruncate the ACVP measurements for < 0.005 m.
Chapter 3
80
3.4.1 Suspended sediment concentrations
3.4.1.1 Time averaged concentrationsFigure 3.4 shows vertical profiles of time averaged suspended sediment concentrations C( ).At x =51.0 m, sediment concentrations were below the OBS detection limit and were thereforediscarded. The different instruments (TSS, OBS, ACVP) generally yield consistent results.Comparison of the different panels reveals a strong cross shore variation in suspendedsediment concentration profiles. At all twelve locations, C( ) follows a rapid decrease withinthe first few cm from the bed, and follows a more gradual decrease at outer flow elevations.Such upward concave profiles on log linear scale are indicative of Rouse shapedconcentration profiles, which have been observed in oscillatory flow tunnel measurementsover plane beds (Ribberink and Al Salem, 1995) and under small scale laboratory breakingwaves (Kobayashi et al., 2005). These profiles can be described with a power function:
C = C0( /za)m (3.4)
where C0 is the time averaged concentration at reference elevation za close to the bed and m isa mixing parameter. Alternatively, exponential distributions for C( ) have been proposed fornon breaking (Nielsen, 1986) and breaking waves (Aagaard and Jensen, 2013). In the presentstudy, C( ) follows an exponential decrease with for parts of the water column, but the fullprofile of C( ) from near bed to water surface is better described through Equation 3.4.
At x = 51.0 m, low concentrations are found throughout the water column (of order 0.1 – 1kg/m3). Much higher concentrations are found in the breaking region at the bar crest (x = 53.0to 55.5 m). At these locations, C( ) is almost depth uniform and is of substantial magnitude(>1 kg/m3) up to wave trough level. Over the shoreward slope of the bar (x = 56.0 and 56.5 m),C( ) shows strong depth dependency with particularly high concentrations (1 to 10 kg/m3) inthe lower half of the water column. Over the bar trough (x = 57.0 to 58.0 m) sedimentconcentrations are much lower than over the bar crest. In the inner surf zone (x = 59.0 to 63.0m), C( ) exponentially decreases between = 0.02 and 0.3 m (i.e. a straight line at this log scale).This is consistent with previous observations over rippled beds (e.g. Nielsen, 1986) andsuggests that ripple vortex suspension controls C( ) in the lower 0.3 m. At higher elevationsC( ) tends to a more depth uniform distribution, which may relate either to enhanced mixingby breaking generated TKE in the higher part of the water column or to arrival of horizontallyadvected suspended sediment.
The strong sediment mixing at the bar crest occurs in the presence of large and energeticbreaking generated vortices (Figure 3.3c). An accompanying experiment with similar bedprofile and the same wave conditions (Ribberink et al., 2014) showed that the near depthuniform concentration profiles above the bar crest extend up to wave crest level, yieldingsignificant concentrations at elevations above wave trough level.
The reference concentration C0 (Equation 3.4) is an important parameter in suspendedsediment transport modeling and is commonly predicted based on the wave plus currentinduced shear stress (Nielsen, 1986; Van Rijn, 2007b). For the present study, the time averagedC0 was estimated at a reference elevation za = 0.005 m by log fitting Equation 3.4 through theACVP measured C( ) between = za and 0.10 m.
Suspended sediment under a breaking wave
81
10-1 100 101
ζ/h
0
0.2
0.4
0.6
0.8
1shoaling zone
wave trough level
x=51.0 m
10-1 100 101
x=53.0 m
10-1 100 101
breaking zonex=54.5 m
10-1 100 101
x=55.0 m
10-1 100 101
x=55.5 m
C (kg/m3)10-1 100 101
x=56.0 m
10-1 100 101
ζ/h
0
0.2
0.4
0.6
0.8
1x=56.5 m
10-1 100 101
x=57.0 m
10-1 100 101
x=58.0 m
10-1 100 101
inner surf zonex=59.0 m
10-1 100 101
x=60.0 m
C (kg/m3)10-1 100 101
x=63.0 m
Figure 3.4. Time averaged sediment concentrations (note log scale for horizontal axis). TSSconcentrations are depicted with grey circles (each circle corresponding to a 15 min. average over arun) and with black dots plus error bars (depicting mean value and standard deviation for a given
nozzle, averaged over all (six) runs per location). Also included are near bed OBS measurements (foreach run; black crosses) and ACVP measurements (only first run, i.e. t=0–15 min.; red line).
Figure 3.5 shows scatter plots of C0 versus rms orbital velocities taken at the velocity overshootelevation (panel a) and versus maximum time averaged TKE in the WBL, kb (panel b).Distinction is made between the region up to the plunge point above the bar crest (x < 55.5 m),the breaking region along the shoreward facing bar slope and bar trough (55.5 x < 59.0 m)and the inner surf zone (x 59.0 m). Figure 3.5a shows that C0 varies by an order of magnitudealong the test section, with much higher C0 in the breaking region along the shoreward facingbar slope than at locations further from the plunge point. Linear regression between C0 andrms revealed no significant correlation (significance level P<0.05). In addition, C0 did not
correlate significantly with estimates of wave plus current induced shear stress (obtainedfollowing Ribberink, 1998) nor with the Sleath parameter that is a measure for pressuregradient induced sediment mobilization (Foster et al., 2006). Note that the poor correlationbetween C0 and rms is particularly caused by the high C0 values in the breaking region betweenx = 55.5 and 57.0 m. When these points are omitted, C0 does correlate significantly with rms, asis to be expected based on previous observations for non breaking waves.
Figure 3.5b shows that C0correlates significantly with kb. In the absence of externally generatedturbulence kb would be related to rms
2 , hence these results suggest that breaking generatedTKE that invades the WBL is an important driver for sediment entrainment. The entrainmentcan be explained physically through large instantaneous bed shear stresses induced by
Chapter 3
82
intermittent TKE arriving at the bed (Cox and Kobayashi, 2000) or through upward directedpressure gradients in the bed under breaking induced vortices (Sumer et al., 2013).
Figure 3.5. Scatter plots of the time averaged reference concentration C0 versus (a) root mean squareorbital velocities at = and (b) maximum time averaged TKE in the WBL, kb. Each measurement point
corresponds to a 15 minute run. Distinction is made between measurements from the shoaling andbreaking region up to bar crest (white squares), the breaking region over the shoreward bar slope and
bar trough (blue circles) and the inner surf zone (red asterisks). In panel (b), the black dashed linecorresponds to a linear relation C0 = 1.7 103 kb while the grey dashed line denotes a quadratic relation
C0 = 1.2 105 kb2.
3.4.1.2 Time varying concentrationsFigure 3.6 shows ACVP measured concentrations <C( ,t)> in the near bed layer from = 0.005m to 0.10 m. The figure includes the phase averaged bed parallel velocities <uR> and near bedTKE <knb> for reference purposes. The overshoot elevation during the crest phase is includedas a proxy for the WBL thickness. The figure also shows depth averaged concentrations (Cnb)over the near bed layer between = 0.005 m and 0.10 m. The Cnb values were normalized bytheir time averaged equivalent to illustrate the relative temporal variation in the near bedsuspended load.
Consistent with results in the previous section, the color contours in Figure 3.6 reveal strongspatial (both horizontally and vertically) variation in concentration. Compared to this spatialvariation, the temporal variation in concentration seems more limited. This holds particularlyfor elevations above the WBL and at locations far from the breaking point (e.g. x = 51.0 m and59.0–63.0 m). The temporal variation was quantified by computing the normalized coefficientsof variation (<C>rms/C), yielding typical values of about 10% above the WBL, but much largervalues (50–80%) inside the WBL. Apparently, the temporal variation in sediment concentrationis mostly restricted to the WBL, whereas outer flow concentrations are fairly constantthroughout the wave cycle.
The shoaling locations (x = 51.0 – 55.0 m) consistently reveal a distinct short duration peak ofincreased sediment concentrations inside the WBL, which occurs between the moment ofoffshore to onshore flow reversal and the moment of maximum <u> during the crest phase.This can be explained by local sediment entrainment during instances of maximum flowvelocity; the suspension events lead the maximum free stream onshore/offshore <u> because
urms (m/s)0 0.2 0.4 0.6 0.8 1
C0 (k
g/m
3 )
0
10
20
30
40
50
60
70 (a)
~kb (m2/s2)
0 0.01 0.02 0.03 0.04
C0 (k
g/m
3 )
0
10
20
30
40
50
60
70 (b)
r2 = 0.51
r2 = 0.58
x < 55.5 m 55.5 ≤ x < 59.0 m x ≥ 59.0 m
Suspended sediment under a breaking wave
83
of the WBL phase lead. Additional processes contributing to high concentrations during thecrest phase are the accumulation of sediment under the wave front by the convergence ofhorizontally advected sediment (Kranenburg et al., 2013), and the vertical sediment advectionby upward periodic velocities during the trough to crest flow reversal (Deigaard et al., 1999).At outer flow elevations ( > ), C increases gradually during the wave trough phase (e.g. at x= 54.5 m from t/T 0.7) and decreases during the crest phase (e.g. at x = 54.5 m from t/T 0.3).
Figure 3.6. Time series of phase averaged near bed velocities, turbulence, and suspended sedimentconcentrations, measured with ACVP at ten locations during t=0–15 min. From top to bottom, each
panel contains: bed parallel velocities at overshoot elevation (blue line); depth averaged (from =0.005to 0.10 m) turbulent kinetic energy <knb> (solid black line); suspended sediment concentrations
(contour in log scale); normalized suspended sediment concentrations, vertically averaged over nearbed layer ( = 0.005 to 0.10 m; red line). The color contour plots contain the time varying bed level
(solid grey line) and the overshoot elevation as proxy for maximum WBL thickness (black dashedline + white triangle).
Chapter 3
84
In the breaking region (x = 55.0 – 59.0 m) the temporal variation in <C> is relatively small. Closeto the plunge point (x = 55.5 – 56.0 m), highest concentrations are found at around the passingof the wave crest. Further shoreward (x = 56.5 – 59.0 m), concentrations are highest during thetrough phase when highest near bed velocity magnitudes are reached. Further into the innersurf zone (at x = 63.0 m) concentrations are slightly higher during the crest phase than duringthe trough phase. In this rippled bed region, it is likely that vortex formation contributes to thehigher concentrations at the wave crest phase (Van der Werf et al., 2007; Hurther and Thorne,2011).
At most locations, <Cnb> is roughly phase coherent with <knb>. It was shown in Chapter 2 that<knb> for the present experiment is not only explained by local processes, i.e. production at thebed or near the water surface and vertical advection/diffusion, but that it is also affected byhorizontal advection. Similarly, we may expect <Cnb> to be affected by a combination of localvertical processes and horizontal advection. Both contributions are quantified in Section 3.4.3.
3.4.2 Cross shore sediment flux
This section analyses the flux components contributing to the total net suspended sedimenttransport. Section 3.4.2.1 analyses the near bed flux, while Section 3.4.2.2 analyzes the flux overthe whole water column.
3.4.2.1 Near bed fluxLocal horizontal sediment fluxes x are the product of velocity u and concentration C and aredecomposed in the same way as velocities into:
x = uC = uC + uC + u C = x + x + x (3.5).
Here, x (current related), x (wave related) and x (turbulent) represent the threecomponents of the total time averaged horizontal sediment flux x. The co located ACVPmeasurements of velocities and sediment concentration enable quantification of all fluxes inEquation 3.5, including the turbulent diffusive flux ’ (see e.g. Naqshband et al., 2014). In thepresent experiment the turbulent flux was measured up to frequencies of about 5 Hz sincehigher frequencies were contaminated by acoustic noise.
Figure 3.7 (color contours) shows phase averaged sediment fluxes < x> in the bed paralleldirection. Highest (onshore/offshore) flux magnitudes occur between x = 53.0 and 56.0 m. Fluxmagnitudes decrease rapidly with distance from the bed, with fluxes outside the WBL up toan order of magnitude lower than fluxes inside the WBL.
Figure 3.7 further shows the time averaged bed parallel fluxes x and the contributions ofeach transport component indicated in Equation 3.5 (2nd and 4th row of panels). At mostlocations, the vertical profile of x shows a sharp transition around = , with much higher x
inside the WBL ( < ) than at outer flow elevations ( > ). At shoaling and breaking locationsbefore the bar crest (x = 51.0 – 55.0 m), wave related fluxes x inside the WBL are directedonshore. This is explained by two processes. Firstly, the velocity and acceleration skewedoscillatory flow leads to higher bed shear during the crest phase and the quasi instantaneous
Suspended sediment under a breaking wave
85
Figure 3.7. Time series of phase averaged bed parallel sediment flux, measured near the bed withACVP at 10 cross shore locations during t=0 15 min. First and third row of panels: bed parallel
velocity at = (blue line); phase averaged bed parallel fluxes < x> (color contours). Second and fourthrow of panels: corresponding vertical profiles of the time averaged bed parallel sediment flux (solid
blue line) and the contributions of three components, i.e. current related (solid grey line), wave related(dashed red line), and turbulent (blue dotted). The horizontal dashed line depicts the WBL overshoot
elevation. Note the varying x scale for the time averaged flux profiles.
response of medium sediment transport leads to an onshore wave related suspension flux inthe WBL (e.g. Schretlen, 2012). Secondly, the free surface effect leads to upward sedimentadvection during the wave upward zero crossing, leading to stretching of the concentrationprofile under the crest and compression during the trough phase which also results in a netonshore directed wave related flux in the WBL (Deigaard et al., 1999; Kranenburg et al., 2013).Current related fluxes x inside the WBL at shoaling locations are offshore directed due to theundertow. The onshore directed wave related fluxes balance (at x = 53.0 m) or exceed (x = 51.0,54.5, 55.0 m) the offshore current related fluxes inside the WBL. Above the WBL, the net flux
x is dominated by the current related component. Although temporal variation in sedimentconcentrations exists above the WBL, it does not result in a significant contribution to the time
Chapter 3
86
averaged wave related fluxes at x = 51.0 – 55.0 m . The different flux behavior inside and abovethe WBL yields a transition from onshore directed x for < to offshore directed x for >.
In the breaking zone, the total net flux x at all elevations is dominated by the current relatedcontribution. Significant contributions of xand ’x occur at x = 56.0 m at both WBL and outerflow elevations. Note that this is the location that is most directly influenced by breakinginduced TKE (Figure 3.3c). The wave related fluxes at this location are directed onshore as thecrest phase concentrations exceed the concentrations during the trough phase. The onshoredirected x counterbalances about 30% of the offshore directed x (depth averaged over =to 0.10 m). x declines much more rapidly than x with distance from the bed. Consequently,at = 0.10 m, the wave related flux is minor (< 10%) compared to the current related flux.Similar to x, the diffusive flux ’x declines rapidly with distance from the bed and it may beneglected outside the near bed region ( > 0.10 m). Time series of diffusive fluxes (not shown)revealed that ’x is predominantly driven by relatively large turbulent events with time scalesof O(1 s). These events likely relate to large scale breaking induced vortices that arrive at thebed, entrain sediment, and carry it onshore and downslope along the shoreward slope of thebar.
In the inner surf zone, x is dominated by the current related flux x, which can be attributedto the strong undertow. The wave related flux remains negligibly small, despite the presenceof orbital sand ripples for which significant wave related flux contributions to total nettransport have been measured for oscillatory conditions without a free stream mean(undertow) current (c.f. van der Werf et al., 2008).
3.4.2.2 Flux over whole water columnThe depth integrated, time averaged suspended transport rate qs is given by
qs=qs,wbl+qs,outer= uCdza
+ uCtfT
d (3.6)crest
where qs,wbl is the net transport rate inside the WBL; qs,outer is the net transport rate over the outerflow; za=0.005 m is the elevation taken to separate suspended and bed load; is the WBLovershoot elevation ( 0.02 m); crest is the wave crest level; and the parameter tf/T is the relative‘wet period’, i.e. the fraction of the wave cycle for which an elevation is immersed. Note that
in Equation 3.6 is defined as the time averaged horizontal velocity over the wet period andnot over the full wave cycle. The ACVP measured fluxes allow direct computation of qs,wbl. Inthe previous section it was shown that outer flow fluxes are dominated by the current relatedcontribution, i.e. x x for > . Therefore, to compute qs,outer, the profile of horizontal fluxesover the complete water column was estimated by vertical inter and extrapolation of timeaveraged velocities and concentrations.
Figure 3.8a shows an example of measured and fitted ( ). Profiles of ( ) were based on acombination of ACVP measurements (for < < 0.10 m) and a semi empirical fit through ADVmeasurements (for >0.10 m). For 0.10 m < < trough, the profile was approximated with aparabolic distribution following undertow approximations by Kobayashi et al. (2005). At
Suspended sediment under a breaking wave
87
elevations above wave trough level, ( ) was approximated through a linear increase with aslope that was chosen such that the time averaged depth integrated mass balance is zero( tf/Td =0crest
0 ). Note that other distributions of ( ) for > trough (e.g. exponential or quadraticincrease) did not result in large differences in the depth integrated suspended transport,because C( ) is nearly depth uniform for > trough. The profile of suspended sedimentconcentrations C( ) in the outer flow was estimated by fitting a Rouse profile (Equation 3.4)through the TSS measurements (Figure 3.8b). Equation 3.4 was log fitted instead of linearlyfitted to reduce a bias towards high concentrations near the bed. The extrapolation of C to
> trough seems justified based on an accompanying experiment (Ribberink et al., 2014) whichincluded TSS measurements between wave trough and crest level. The relative wet period tf/Twas extracted from PT measured water surface levels (Figure 3.8c). The product of these threeterms yields the time averaged x profile (Figure 3.8d), used for the estimation of qs,outer inEquation 3.6.
Figure 3.8. Example of outer flow sediment flux calculation near the breaker bar at x = 54.5 m: (a)Time averaged horizontal velocities, measured with ADVs (filled circles) and ACVP (dots), and fitted
values (dashed line); (b) Time averaged sediment concentrations, measured with TSS (circles) andpower function fit (dashed line); (c) Relative ‘wet period’ tf/T; (d) Current related sediment flux profile
x( ), as the product of the dashed lines in panels a c.
Figure 3.9b shows the resulting vertical profiles of the approximated net suspended sedimentflux ( x) at seven cross shore locations. Figure 3.9c shows the spatial flux distribution andincludes the elevations below which 50% and 90% of the flux is found. These levels are basedon the depth integrated absolute values of the flux | x|dcrest
za. Note that the fluxes x inside
the WBL (Figure 3.7) are significantly higher than the outer flow fluxes. Hence, forpresentation purposes, the WBL fluxes are omitted in Figure 3.9b c. Figure 3.9a shows theundertow profiles for reference.
At x = 51.0 m, x is much lower at outer flow elevations than inside the WBL. In the breakingregion at the bar crest (x = 53.0 to 55.5 m), i.e. between break point and plunge point, significantx contributions to qs occur between wave trough and wave crest level. This is attributed to
strong vertical mixing of suspended sediment in combination with relatively shallow waterdepths. At these locations the onshore directed fluxes between trough and crest counterbalancea large portion (about 70%) of the offshore directed flux below wave trough level. The highest
u (m/s)-1 0 1 2
ζ/h
0
0.5
1
1.5
xηtrough
ηcrest(a)
C (kg/m3)0 1 2 3
x
(b)
tf/T0 0.5 1
=
(c)
φx (kg/m2s)-0.5 0 0.5
(d)
Chapter 3
88
offshore directed fluxes are found along the shoreward facing bar slope (x = 55.5 to 57.0 m) inthe lower 0.2 m above the bed. This relates to the combination of high near bed concentrationsand the shape of the undertow profile, with strong offshore directed (up to –0.8 m/s) closeto the bed (Figure 3.9a). Along the bar trough and inner surf zone (x > 57.0 m), fluxes within0.3 m from the bed are the main (>50%) contributors to qs while fluxes above trough level areminor (<10% of qs).
Figure 3.9. Vertical distribution of net suspended sediment horizontal flux x. (a) Time averagedhorizontal velocities, measured with ADV (squares) and ACVP (dots); (b) Vertical profiles of x at
seven locations halfway through the experiment (t=45 – 60 min.); (c) Color contour plot of x for t=45 –60 min. For presentation purposes, panels a b do not show all 12 measurement locations and panels b
c do not include the fluxes inside the WBL. White squares in panel (c) mark elevations where theintegrated flux from the bed upwards reaches 50% and 90% of the depth integrated absolute x from
= za to crest (values are averaged over six runs, with error bars marking the 95% confidence interval).The bed profile corresponds to t=45 min.
Suspended sediment under a breaking wave
89
q s (m3 /m
2 s)
×10-5
-10
-5
0
5(a)
qs,outerqs,wbl
f
0
0.2
0.4
0.6
0.8
1(b)
fwblfouter
x (m)50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
z (m
)
-1.5
-1
-0.5(c)
0 min.90 min.
Figure 3.10a shows the depth integrated net suspended transport rate within the WBL (qs,wbl)and over the outer flow (qs,outer) following Equation 3.6 along the bed profile. The relativeimportance of qs,wbland qs,outer to total suspended transport is quantified by relative fractions fwbland fouter, based on the sum of the absolute values of both contributions (i.e. fwbl =|qwbl|/(|qwbl|+|qouter|) and fouter = 1 fwbl). Figure 3.10b shows the cross shore variation in theserelative fractions.
Figure 3.10. Cross shore variation in depth integrated total net suspended transport inside the WBLand in the outer flow. (a) Suspended transport rates inside the WBL (blue triangles and solid line) and
in the outer flow (grey squares and dashed line). (b) Relative fraction of transport inside the WBL(blue) and in the outer flow (grey); (c) Bed profiles at 0 and 90 min. Results are averaged over six runs
with error bars in (a) marking one standard deviation of the mean.
The magnitude of qs,outer increases strongly from x = 51.0 to 53.0 m, due to increasingconcentrations and undertow magnitudes (Figure 3.10a). Between x = 53.0 and 55.5 m, qs,outerremains roughly constant which is partly due to the increasing significance of transport for> trough. Along the shoreward facing bar slope (x = 56.0 – 57.5 m), qs,outer magnitudes increase
rapidly due to the large offshore directed fluxes close to the bed. qs,outer magnitudes decreasegradually along the inner surf zone as suspended sediment concentrations decrease.
The suspended transport inside the WBL (qs,wbl) is onshore directed in the shoaling zone andin the breaking region up to the bar crest (x = 51.0–55.0 m), indicating that onshore waverelated transport contributions generally exceed the offshore directed current relatedtransport inside the WBL. The relative contribution of qs,wbl to total suspended transport atshoaling locations is about 10–20% (Figure 3.10b). Note that qs,wbl is formed by two transportcomponents of similar magnitude but with opposite sign, which partly explains why fwbl issmall. Both qs,wbl and fwbl increase gradually from the shoaling zone to the bar crest, with
Chapter 3
90
maximum onshore transport found at the bar crest (x = 55.0 m). In the breaking region alongthe shoreward slope of the bar (x = 55.5 – 57.0 m), qs,wbl becomes offshore directed and itsmagnitude increases. Also the fraction of transport confined to the WBL increases slightly,with an fwbl of about 20–30 %. At the bar trough and inner surf zone (x = 58.0 – 63.0 m), |qs,wbl|decreases and the total suspended transport is largely (> 80 90%) determined by the outerflow transport.
3.4.3 Cross shore advection, pick up, and deposition
The flux measurements presented earlier are used in this section to study the cross shoreadvection of sediment in relation to the vertical sediment exchange between the suspensionand bedload layer (pick up/deposition) at a wave averaged time scale (Section 3.4.3.2) and atan intra wave time scale (Section 3.4.3.3).
3.4.3.1 CalculationsWe introduce a sediment mass balance for a control near the bed (Figure 3.11), given by
<C( ,t)>t
dD
za+
< x ,t >x
dD
za
< z ,t >z
d = 0D
za(3.7)
where < x> and < z> are the phase averaged ACVP measured total fluxes in the horizontaland vertical direction, respectively. The control volume extends vertically from = za = 0.005m up to = D = 0.10 m and matches the near bed layer covered by the ACVP. It follows fromEquation 3.7 that local concentration changes (term 1) are the result of horizontal gradients incross shore sediment flux, i.e. horizontal sediment advection (term 2), and of vertical gradientsin the vertical sediment flux (term 3).
Equation 3.7 was evaluated at each cross shore location using a central difference scheme inboth time and space, with a time step t equal to 0.05 s and spatial step size x equal to thedistance between adjacent measurement locations (i.e. 0.5 m in the breaking zone and up to 3m in the inner surf zone, c.f. Table 3.1). Concentrations and vertical fluxes are weightedaverages of measurements at the x location of interest and at the onshore and offshore adjacentlocations. The horizontal gradient in sediment flux is calculated over location x using < x>measurements at the two adjacent locations. x is of similar magnitude as the semi excursionlength a and much smaller than the wave length L ( 15 m). It is therefore considered sufficientsmall to estimate the horizontal flux gradients with appropriate accuracy. Nevertheless, it isacknowledged that the finite number of cross shore measurement locations leads tosmoothing of the actual gradients in flux. The horizontal flux gradient cannot be estimated forthe furthest offshore and onshore locations. For these locations we assume negligiblecontribution by horizontal advection because of the low cross shore gradients in suspendedsediment concentration and in qs compared to the strongly non uniform concentrations andtransport rates in the breaking region.
Suspended sediment under a breaking wave
91
Bed
Bedload layer
d〈C〉/dt
〈Φz(D)〉
〈Φz(za)〉
〈Φ〉x, left 〈Φ〉x, rightNear-bed
Outer flow
ζ=za
ζ=D
xleft xrightx
Figure 3.11. Definition sketch of control volume and fluxes. The control volume extends verticallyfrom za (=0.005 m) to D (=0.10 m).
The depth integrated vertical gradient in vertical flux (term 3 in Equation 3.7) equals thedifference between the vertical flux at the bottom of the control volume < z(za)> and the fluxat the top < z(D)>. However, the vertical velocities very close to the bed were not properlyresolved by the ACVP (Chapter 2), leading to errors in < z(za)>. Therefore, an alternativeapproach was adopted as follows. The first two terms of Equation 3.7 were determined fromthe data and the third term then follows from the mass balance. This term can be rewritten as
< z ,t >z
dD
za< z D > < z za > (3.8)
which, in combination with measured < z(D)>, allows < z(za)> to be solved. z(za) is thevertical exchange between the bedload layer ( < za) and the suspension layer ( > za). It can bedecomposed into a deposition rate d (defined positively downward) and a pick up rate p(defined positively upward). Under an assumption of free settling, which seems appropriatefor medium grained particles at concentrations of O(1–10) kg/m3 (e.g. Baldock et al., 2004), thedeposition rate was modeled as d = wsC(za) (Nielsen, 1992). The pick up rate is then given by p= d + z(za). Because p and d were not directly measured and are based on a modelingassumption for the deposition rate, estimations of p and d following the above approachshould be interpreted with caution. For this reason they are evaluated at a wave averaged timescale only in what follows, i.e.:
z za = p d = p wsC(za) (3.9).
3.4.3.2 Time averaged pick up, deposition and horizontal gradients in cross shore transportAt a wave averaged time scale and for equilibrium conditions, dC/dt = 0 and the vertical fluxbetween the bedload and suspension layer z za should equal the cross shore gradient insuspended transport rate, i.e.
z za =dqsdx
(3.10)
where qs is the net total transport rate over the complete water column (Equation 3.6). Figure3.12a shows both terms of Equation 3.10, with z(za) obtained using Equation 3.8 timeaveraged. Although the approaches for the two quantities are subjected to different
Chapter 3
92
assumptions in data treatment, the validity of both approaches (Equation 3.6 and Equation3.8) is supported by the consistent results in terms of magnitude and cross shore behavior.
Figure 3.12. (a) Time averaged vertical flux between bedload and suspension layer at z=za, estimatedfrom control volume analysis using ACVP measurements (red triangles), and cross shore gradient oftotal depth integrated (from =za to crest) suspended load (black squares); (b) Time averaged pick up(blue squares) and deposition rates (red triangles); (c) maximum time averaged TKE inside the WBL
( < ); (d) Bed profile measurements at t=0 min. (solid) and t=90 min. (dashed), for reference. Values in(a c) are means over six runs, with error bars in (a b) marking standard deviation of mean.
z(za) can be interpreted as the contribution of suspended transport to the time rate ofmorphological change of the bar, with z(za)<0 (net downward flux) corresponding to localaccretion and z(za)>0 to erosion. If z(za) = 0, there is no cross shore gradient in suspendedtransport and time averaged local pick up balances deposition. The highest magnitudes ofz(za) occur between x = 54.0 and 58.0 m (Figure 3.12a). This relates directly to the strongly
non uniform hydrodynamics in cross shore direction due to wave breaking and due to crossshore varying water depths, which lead to steep cross shore gradients in suspended sedimentconcentrations and suspended transport rates. Net suspended sediment pick up ( z(za)>0)occurs at the shoreward slope of the bar and over the bar trough (x = 56.5 to 58.0 m) while netsediment deposition ( z(za)<0) occurs around the bar crest (x = 53.0 to 56.0 m). Between theseregions, the undertow drives net offshore advection of suspended sediment from the bar
Φz(z
a) (kg
/m2 s)
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
net pick-up
net deposition
(a)
plunge point
Φz(za)dqs/dx
p, d
(kg/
m2 s)
0
1
2
3
4
5(b)
pick-up ratedeposition rate
k b (m2 /s
2 )
0
0.005
0.01
0.015
0.02 (c)
x (m)50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
z (m
)
-1.5
-1
-0.5 (d)0 min.90 min.
Suspended sediment under a breaking wave
93
trough to the bar crest. Note that the regions of net pick up and net deposition are roughlyconsistent with net erosion and accretion regions of the bed profile (Figure 3.12d). However,the profile evolution can only be fully explained by also considering the gradients in bedloadtransport.
Figure 3.12b shows the time averaged pick up (p) and deposition (d) rates, obtained throughdecomposition of z(za) through Equation 3.9. The high pick up rates in the vicinity of theplunge point (between bar crest and bar trough) are prominent, with values that are two tofive times the pick up rates in the shoaling zone. The cross shore variation in pick up (Figure3.12b) does not match the cross shore variation in maximum onshore/offshore velocities,which decrease in the breaking region (Figure 3.3b). The pick up variation shows a bettersimilarity with the cross shore variation in near bed TKE (Figure 3.12c), which is consistentwith the results for reference concentrations discussed earlier (Section 3.4.1.1).
Sediment deposition and pick up rates are of similar magnitude at all locations. The smalldifference between p and d, i.e. the net vertical flux z(za), is due to the influx of horizontallyadvected sediment. The contribution by horizontal sediment influx to local d is rather weak,i.e. typically less than 10%, compared to contributions by locally entrained sediment given byp. From this it follows that the time averaged local deposition rate, and consequently thereference concentration C0=C(za), is largely controlled by local pick up.
3.4.3.3 Horizontal advection and vertical flux contributions to intra wave concentration changesThe time varying concentration behavior in the near bed region, presented earlier in Figure3.6, can be explained in terms of cross shore and vertical fluxes by solving Equation 3.7 at anintra wave time scale. For convenience, Equation 3.7 is rewritten as:
<mnb>t
<qnb>x
+ < z za > < z D > (3.11)
Here, mnb is the depth integrated suspended sediment load over the control volume (i.e. mnb =C dD
za= Cnb (D – za); qnb is the time varying depth averaged horizontal suspended transport
rate over = za to D; z(za) is the vertical flux at = za and z(za) is the vertical flux at = D.Because of the strong decrease in concentration with distance from the bed, the magnitudes ofintra wave < z(za)> exceed < z(D)> with a factor 5 to 10 (i.e. | (za)| >> | (D)|). This allowsEquation 3.11 to be rewritten as:
<mnb>t
<qnb>x
+ < z za > qnb + < z za > (3.12)
The flux gradient qnb is termed the horizontal influx. Note that qnb is defined as the negativecross shore gradient in near bed suspended transport rate qnb, i.e. positive qnb corresponds toan increase in the suspended load mnb. Equation 3.12 states that temporal changes in the nearbed suspended load are primarily caused by horizontal sediment advection and by verticalexchange between the bedload layer and suspension layer. The vertical influx at = D hasminor effect on mnb at an intra wave time scale and is not considered in the following analysisof <mnb>/ t.
Chapter 3
94
Figure 3.13. Spatio temporal variation in phase averaged near bed concentrations in relation tohydrodynamics and gradients in horizontal and vertical flux, for t=0 15 min. (a) Bed parallel velocitiesat = ; (b) Free stream turbulent kinetic energy at =0.11 m, measured with ADV; (c) Depth averaged( = za to 0.10 m) near bed concentrations in log scale; (d) Rate of change of near bed concentrations;(e) Sediment influx due to horizontal advection; (f) Vertical sediment influx from bedload layer; (g)
Reference bed profile. Fluxes in e f contain contributions of all transport components (current, wave,turbulent). Panels a f include reference lines (dotted) depicting zero up crossings of water surface
level, marking reversal between wave crest and trough phase (dotted). In the analysis distinction ismade between three regions, divided by vertical grey lines in all panels (see text).
Figure 3.13 shows the spatio temporal variation in the depth integrated mass <mnb> over thenear bed layer (panel c) and its time rate of change <mnb>/ t (panel d), which relates to the
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horizontal influx qnb (panel e) and the vertical influx z(za) (panel f) that were quantified asdescribed in Section 3.4.3.1. For reference, the figure includes the phase averaged bed parallelvelocities (panel a) and the free stream ADV measured TKE at =0.11 (corresponding roughlyto the top of the control volume; panel b). Each panel includes the upward and downwardzero crossings of the water surface level (dotted lines) as a phase reference. The wavespropagate through the spatiotemporal domain from the lower left to the upper right corner.
Comparison of Figure 3.13e and Figure 3.13f reveals that qnb and z(za) are of similarmagnitude. Hence, both the horizontal sediment influx along the bed and the vertical influxbetween the bedload and suspension layer induce temporal changes in the suspended mass(Figure 3.13d).
Between x = 51.0 and 55.0 m, i.e. at the shoaling and breaking region up to the bar crest, mnbincreases (positive mnb/ t in Figure 3.13d) between the middle of the wave trough phase untilshortly after flow reversal and decreases during the wave crest phase (negative mnb/ t).Figure 3.13f shows that these temporal changes are partly explained by vertical influx fromthe bedload into the suspension layer, with z(za)>0 around the zero up crossing whenperiodic velocities are directed upward and sediment is entrained, and z(za)<0 during thecrest phase when suspended particles settle down. The phase behavior of mnb/ t is furtherexplained by the horizontal sediment influx qnb (Figure 3.13e). During the wave trough phase,suspended sediment is advected offshore from the high concentration breaking region to thelow concentration shoaling zone, leading to a positive influx of sediment ( qnb>0) and anincrease in suspended mass at x = 51.0 to 55.0 m. During the wave crest phase, a reverse patternoccurs as suspended particles are advected onshore from the shoaling to the breaking zone,leading to qnb<0 and a decrease in mnb. This excursion of suspended sediment betweenbreaking and shoaling locations explains the concentration changes above the WBL ( > ) thatwere previously identified in Figure 3.6 (at x = 53.0 – 55.0 m).
In the breaking region between bar crest and bar trough (x = 55.5 to 58.0 m), the temporalbehavior of horizontal and vertical advection differs notably from the locations offshore fromthe bar crest. Figure 3.13f shows that at the bar trough (x = 57.0 – 58.0 m), a positive verticalinflux from the bedload to the suspension layer occurs during most of the wave trough phase(t/T 0.75 to 0.25 in next wave cycle). This net pick up at the bar trough is due to thecombination of the large offshore directed velocities (Figure 3.13a) and the presence ofbreaking generated TKE that arrives at the bed during the wave trough phase (Figure 3.13b).Phase averaged velocities are almost continuously directed offshore at these locations, leadingto rapid offshore advection of the entrained sediment along the steep shoreward slope of thebar towards the bar crest. This explains the predominantly negative horizontal influx (i.e.removal of sediment) at the bar trough (x = 56.5 to 57.5 m; Figure 3.13e). This offshore advectedsediment arrives at the bar crest (x = 55.5 – 56.0 m), leading to a positive horizontal influxduring most of the wave cycle (Figure 3.13e). This positive horizontal influx is accompaniedby a negative vertical influx near the bar crest (Figure 3.13f) which indicates net deposition ofsuspended sediment. This deposition occurs particularly during the wave crest phase, whensediment concentrations are highest.
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At the inner surf zone the temporal changes in suspended mass mnb/ t are much smaller thanat the shoaling and breaking locations; no distinct patterns in horizontal and vertical sedimentinflux are identified.
3.5 Discussion
Near bed concentration changes are not only due to local pick up and deposition processes,but are also due to horizontal influx of sediment that results from cross shore non uniformityin the horizontal sediment fluxes. The latter also occurs in WBLs under non breaking wavesbecause the velocity field changes in space and time as a wave progresses. Kranenburg et al.(2013) showed that horizontal sediment fluxes converge during the wave crest phase anddiverge during the wave trough phase, leading to highest concentrations under the wave crestand lowest concentrations under the wave trough. Compared to these non breaking waveobservations, the phase behavior at shoaling locations in the present study is slightly shifted:maximum concentrations are reached around trough to crest flow reversal, i.e. before thepassing of the wave crest and at an earlier stage than under non breaking waves. This isexplained by the strong cross shore variation in suspended sediment concentrations insideand outside the WBL near the breaking point, leading to a much higher influx of sedimentduring the wave trough phase (arrival of high concentration) and an earlier local maximum insuspended sediment concentrations.
The observed offshore onshore excursion of suspended sediment between the breaking andshoaling zone is consistent with field observations under plunging breakers by Beach andSternberg (1996), who observed a ‘cloud of sediment sweeping back and forth’. Note that thesuspended sediment that enters the shoaling zone during the trough phase roughly balancesthe sediment leaving the shoaling zone during the crest phase (Figure 3.13e). Hence, sedimentparticles seem to remain in suspension – or the settling of suspended particles balances theentrainment of particles from the bedload layer – during the complete wave cycle whilefollowing the orbital flow. This sediment excursion is consistent with the excursion of TKEhighlighted in Chapter 2, suggesting that suspended sediment particles are trapped inturbulent vortices that are partly breaking generated. It has been suggested that the phasecoupling of TKE and suspended sediment concentrations under plunging breakers mayenhance the wave related suspended sediment transport (Ting and Kirby, 1994; Boers, 2005;De Serio and Mossa, 2006). However, in the present study, the particles trapped in turbulentvortices are advected back and forth, resulting in local (Eulerian) concentration changes butgenerally not in a net wave related transport contribution at elevations outside the WBL. Thisrelates directly to the relatively low intra wave variation in TKE for the present conditions:TKE does not decay fully within a wave period and significant residual turbulence persistsinto the next wave cycle (Van der A et al., Submitted). This high residual turbulence (comparedto small scale plunging breaking wave studies with equivalent Froude scaled wave period)may relate to the breaker bar presence, which contributes to flow non uniformity and velocitystrain rates that contribute to turbulence production in the water column (Van der A et al.,submitted). It is anticipated that for longer period or random waves, which yield strongertemporal variation in TKE than the waves in the present study, the outer flow wave relatedsuspension fluxes could be of higher significance. The latter may also explain why field
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measurements at fine to medium sand beaches have shown significant wave related fluxes atouter flow elevations in the breaking region (Osborne and Greenwood, 1992; Ogston andSternberg, 1995; Ruessink et al., 1998).
Outer flow concentration profiles above the breaker bar crest are approximately depthuniform and high sediment concentrations occur in the outer flow up to wave crest level. Thesehigh concentrations are not only explained by vertical mixing by orbital velocities and(breaking generated) turbulence, but also by vertical advective sediment fluxes due to nonzero time averaged vertical resulting from (i) a vertical component of the undertow as itfollows the bar geometry, and (ii) cross shore gradients in the bed parallel undertow velocitiesthat are balanced by a velocity in bed normal direction (i.e. because of fluid massconservation). For the present study, time averaged velocities follow a circulation cell withdownward velocities above the bar trough and upward velocities above the bar crest (Van derA et al., submitted). In morphodynamic models all three mixing mechanisms (turbulent, waverelated, time averaged advection) should be taken into account. This also holds for thesignificant contribution of suspended sediment flux occurring between wave trough and wavecrest level observed in the present study.
In terms of sand transport modeling, empirical formulations for enhanced wave relatedsuspended transport reaching elevations far outside the WBL have been proposed for thebreaking region (Van Rijn, 2007b). This approach is partly supported by the presentmeasurements. Indeed, the magnitude of the wave related transport is enhanced in thebreaking region, especially at the bar crest, compared to the shoaling zone (Figure 3.7; Figure3.10a). However, the wave related fluxes generally do not extend vertically into the outer flow,but remain confined to the WBL as is also the case for non breaking waves (c.f. Schretlen, 2012).An exception is one location along the shoreward bar slope, where near bed TKE is highestand where significant wave related transport occurs above the WBL.
Time averaged near bed concentrations are largely controlled by local pick up. Mostcommonly used formulae for reference concentration C0 are based on estimates of bed shearstress by periodic and time averaged near bed velocities (e.g. Nielsen, 1986; Van Rijn, 2007b)and will likely predict highest pick up and offshore directed suspended transport rates at thebar crest (c.f. Jacobsen and Fredsoe, 2014). In the present study, maximum pick up rates arefound shoreward from the bar crest along the shoreward facing bar slope, where highest nearbed TKE occurs. Consistent with other surf zone observations (e.g. Voulgaris and Collins, 2000;Aagaard and Jensen, 2013), the present study shows that C0 correlates poorly with and rms.Hence, the cross shore variation in sediment pick up cannot be explained by bed shear stresspurely by periodic and time averaged velocities. Instead, C0 correlates significantly with nearbed TKE, suggesting that breaking generated turbulence is an important driver for sedimentpick up.
This implies that C0 models in the breaking zone can be considerably improved throughparameterizations of near bed turbulence effects on sediment entrainment. Although suchmodels have already been proposed (e.g. Steetzel, 1993), it should be noted that it is not trivialto quantify near bed TKE using existing turbulence closure models (Brown et al., 2016). Analternative is a C0 model that is based on breaking wave characteristics such as the relativewave height (Mocke and Smith, 1992) or wave energy dissipation due to breaking (Kobayashi
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and Johnson, 2001). However, the present study shows that near bed TKE is not fullydetermined by local 1D processes, i.e. production at the bed and water surface followed byvertical advection/diffusion; instead, TKE spreads in the cross shore direction throughadvection by the undertow and orbital flow and by diffusion (van der Zanden et al., 2016; vander A et al., submitted). Consequently, the region at which sediment pick up is enhancedextends to shoaling locations adjacent to the breaking zone (see Figure 3.12bc). Thedevelopment of C0 formulations for surf zone conditions would likely benefit from highresolution data of near bed concentrations, turbulence, and wave characteristics for a widerrange of breaking wave conditions and sediment characteristics than covered by the presentand previous studies.
3.6 Conclusions
The effects of wave breaking on suspended sediment processes were examined through alarge scale wave flume experiment, involving regular plunging breaking waves over a barredbeach of medium sand. Measurements of suspended sediment concentrations and fluxes wereobtained at 12 locations from the shoaling to the inner surf zone and extend a large part of thewater column, with particularly high resolution in the lowest 0.10 m that includes the wavebottom boundary layer (WBL). The measurements were related to observations of near bedhydrodynamics including turbulent kinetic energy (TKE), as presented inChapter 2, and yieldnew insights into sediment pick up, deposition and horizontal advection in the breakingregion. Based on the results we conclude the following:
1. Breaking generated TKE that invades the WBL has a significant effect on near bedsediment concentrations. Sediment pick up rates increase by an order of magnitudebetween the shoaling and breaking regions. Wave averaged reference concentrations inthe breaking region correlate better with near bed TKE than with bed parallel periodicvelocities, suggesting that breaking generated turbulence is an important driver forsediment pick up. At an intra wave time scale, suspended sediment concentrations aregenerally phase coherent with near bed TKE.
2. Sediment concentration profiles are Rouse shaped with a strong increase in concentrationinside the WBL. Suspended sediment is particularly strongly mixed above the bar crest,where outer flow concentrations are nearly depth uniform. This vertical mixing isattributed to the combination of energetic breaking generated vortices, the stronglyasymmetric wave shape (strong upward wave related advection), and upward directedwave averaged velocities resulting from a time averaged fluid circulation cell.
3. Net (i.e. wave averaged) suspended sediment fluxes reveal a complex pattern withalternating onshore and offshore directed constituents. In the shoaling region andbreaking locations up to the bar crest, net sediment fluxes are directed onshore inside theWBL but offshore in the outer flow. Above the breaker bar crest a substantial onshoredirected suspended transport contribution occurs above wave trough level. In the breakingregion along the shoreward slope of the bar and inside the inner surf zone, net suspendedsediment fluxes are offshore directed over most of the water column.
4. Net outer flow suspended fluxes are generally current related and offshore directed dueto the undertow. Significant net wave related fluxes are observed at shoaling and breaking
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locations, where they are directed onshore and are generally confined to the WBL. Only atone location, i.e. the breaker location with highest near bed TKE and near bedconcentrations, does the net wave related flux extend vertically to outer flow elevations.
5. Sediment flux gradients were quantified to study the advection and the pick up anddeposition of suspended sediment. At a wave averaged time scale, sediment grains areentrained from the bed in the bar trough region, are advected offshore by the undertow,and are deposited in the region covering the shoaling zone, bar crest, and the upper partof the steep onshore bar slope. Near bed concentrations are largely (>90%) determined bylocal pick up; contributions of cross shore advected sediment are minor.
6. Offshore from the bar crest, concentration changes are primarily due to cross shoreadvection by orbital velocities. Suspended particles travel back and forth between thebreaking and shoaling zone, yielding an increase in sediment concentrations at shoalinglocations during the wave trough phase and a decrease in concentrations during the wavecrest phase. This onshore offshore excursion is consistent with the spatio temporalvariation in TKE, which suggests that sediment particles are trapped in breakinggenerated vortices that are advected back and forth following the orbital motion.
7. Shoreward from the bar crest, concentration changes are due to cross shore varying andtime varying pick up and deposition rates and due to cross shore gradients in periodicand time averaged velocities. Sediment is entrained in the bar trough especially during thewave trough phase, when both near bed velocity magnitude and breaking generated TKEarriving at the bed are highest. The entrained particles are almost instantly advectedoffshore and are deposited near the bar crest during the wave crest phase when velocitymagnitudes reduce.
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4 Bedload and suspended loadcontributions to themorphodynamics of a large scalelaboratory breaker bar
Highlights:
Sheet flow layer dynamics at breaker bar crest are not affected by breaking generatedturbulence but are affected by horizontal sediment influx from adjacent locations.
Onshore bedload and offshore suspended load transport are of similar magnitude butof opposite sign.
Bedload and suspended load transport have opposite effects on breaker bar growthand migration.
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Abstract
This chapter presents measurements of sheet flow processes, grain sorting, and bedload plussuspended load transport rates around a medium sand breaker bar in a large scale waveflume. The results offer insights in effects of wave breaking on bedload and grain sortingprocesses and in the quantitative contribtions by bedload and suspended transport to breakerbar morphodynamics. The quasi instantaneous sheet flow response to phase averagedvelocity is consistent with observations under non breaking waves. The sheet flow layerthickness is locally somewhat higher than expected based on hydrodynamic forcing, which isattributed to a net horizontal sediment influx (i.e. due to non uniform cross shore advection).The cross shore variation in bedload transport rates relates to variations in wave shape (i.e.velocity skewness and asymmetry) at locations covering the shoaling region up to the bar crest.At locations between bar crest and bar trough, bedload transport correlates positively withbed slope and turbulent kinetic energy. Bedload and suspended load transport rates are ofsimilar magnitude but of opposite sign. Bedload transport is onshore directed and dominatesat the shoaling zone, but following wave breaking, the offshore directed suspended sedimenttransport increases in magnitude and exceeds bedload transport rates at the breaking andinner surf zone. Bedload and suspended load transport contribute notably differently to bedprofile evolution: bedload transfers sand grains from the offshore slope to the bar crest andadditionally leads to erosion of the shoreward bar slope and deposition at the bar trough,while suspended load transport induces an opposite pattern of erosion at the bar trough andaccretion at the bar crest. Suspended grain samples reveal size selective entrainment andvertical size segregation at the inner surf zone, but suggest size indifferent entrainment andvertical mixing by energetic vortices in the breaking region. Size selective transport as bedloadand suspended load leads to a cross shore coarsening of the bed from shoaling to inner surfzone, with local additional sorting mechanisms around the breaker bar due to bed slopeeffects.
This chapter is in preparation for submission as:
Van der Zanden, J., van der A, D. A., Hurther, D., Cáceres, I., O’Donoghue, T., Hulscher, S. J.M. H. and Ribberink, J. S. Bedload and suspended load contributions to the morphodynamics of alarge scale laboratory breaker bar.
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4.1 Introduction
Breaker bars are morphologic features that are formed naturally in wave breaking zones ofdissipative and intermediate beaches (Wright and Short, 1984). Breaker bars enhance waveenergy dissipation due to breaking and are one of the factors that determine the state of thebeach profile (Lippmann and Holman, 1990; Wijnberg and Kroon, 2002; Price and Ruessink,2011). Breaker bars are dynamic and tend to migrate offshore during storm conditions, whenstrong wave breaking occurs, and onshore during mild wave conditions (Thornton et al., 1996;Ruessink et al., 2007). The offshore migration is attributed to an increase in both undertowvelocities and suspended sediment concentrations as the intensity of wave breaking increases,which enhances offshore directed suspended sediment transport (Sallenger et al., 1985;Thornton et al., 1996). Onshore migration is explained by the vertically and horizontallyasymmetric shape of the shoaled waves, leading to higher magnitudes of near bed orbitalvelocities (velocity skewness) and of fluid accelerations (acceleration skewness) during thecrest phase relative to the trough phase, which both favor onshore directed wave relatedsediment transport near the bed (Elgar et al., 2001; Hoefel and Elgar, 2003).
By including contributions of offshore directed current related and onshore directed waverelated sediment transport, numerical models can predict on and offshore bar migrationreasonably well (Henderson et al., 2004; Hsu et al., 2006; Dubarbier et al., 2015; Fernández Moraet al., 2015). However, sediment transport predictions in these models are usually onlyvalidated on bed profile evolution and may not adequately represent the individualcontributions by net bedload and suspended load transport. In addition, the effects of wavebreaking on sediment transport rates are not fully understood and therefore often neglected.In order to improve understanding and numerical modeling of breaker bar evolution, it isrelevant to study how wave breaking affects bedload transport processes at intra wave andwave averaged time scales.
Previous research has shown that large scale wave breaking enhances turbulence levels overthe entire water column including the wave bottom boundary layer (Chapter 2). This explainsobservations of enhanced instantaneous bed shear stresses (Cox and Kobayashi, 2000; Sumeret al., 2013) and suspended sediment entrainment rates (Nielsen, 1984; Chapter 3) underbreaking waves. The presence of additional turbulence may also increase bedload transportrates, as shown for a steady flow with artificial grid turbulence (Sumer et al., 2003), but itshould be noted that the latter experiment involved mild flow conditions with a bedloadtransport regime that differs significantly from the sheet flow conditions under full scalebreaking waves (Nielsen, 1992). Bedload in sheet flow conditions has been extensively studiedin wave flumes under non breaking waves (Dohmen Janssen and Hanes, 2002; Schretlen,2012) and oscillatory flow tunnels (see van der Werf et al., 2009, for an overview). Observationsin the swash zone revealed that bore turbulence and cross shore sediment advection may leadto increased sheet flow layer thicknesses compared to non breaking wave observations (vander Zanden et al., 2015a; Lanckriet and Puleo, 2015). Due to a lack of high resolutionmeasurements, it is still unclear if and how wave breaking affects sheet flow transport ratesand processes around the breaker bar. Consequently, it is also unclear whether existingengineering type bedload transport formulae, used for morphodynamic simulations, shouldaccount for wave breaking effects (Van Rijn et al., 2013). Therefore, the first motivation of thepresent study is to explore bedload processes across the wave breaking zone.
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Research has further revealed that transport in the breaking region is size selective, i.e. differsfor each grain size class within a sediment sample. Observations of graded sediment transportunder oscillatory sheet flow conditions have shown that coarser grains are transported moreeasily than finer grains because they are more exposed (de Meijer et al., 2002; Hassan andRibberink, 2005). The suspended load transport generally contains a relatively high fraction offine grained particles which are more easily entrained and mixed than coarse grains (Nielsen,1992; Wiberg et al., 1994; Davies and Thorne, 2016) and which are advected by the mean current(Sistermans, 2002). In time, the removal of fine grained particles from the bed may lead tocoarsening of the seabed’s top layer. This may even lead to the formation of erosion resistantbed surface layers of coarse grains (‘armouring’), which can significantly reduce sedimentpick up and transport rates (Nielsen, 1992; Wiberg et al., 1994). Finn et al. (2016) suggest, basedon detailed simulations with a particle based numerical model, that such armour layers forsheet flow conditions may already develop after one wave cycle. Grain size observations infield (Wang et al., 1998) and laboratory (Koomans, 2000) conditions revealed a relatively largefraction of coarse sand on breaker bar crests, while bar troughs are composed of relatively finesediment. The transport of graded particles can be modelled by calculating transport fordifferent grain classes independently (e.g. Reniers et al., 2013), with the optional inclusion of a‘hiding and exposure’ factor that accounts for reduced or enhanced exposure of certain grainclasses (e.g. Van Rijn, 2007c). The inclusion of size selective transport can significantly alternumerical predictions of breaker bar position and shape compared to simulations withuniform sand (Van Rijn, 1998). This illustrates the relevance of grain sorting processes for theunderstanding and modeling of breaker bar morphodynamics; yet no study has examined thetemporal evolution of a breaker bar’s grain composition in relation to measured suspendedand bedload transport rates. This forms the second motivation of the present study.
This study presents high resolution measurements of sand transport processes under a largescale laboratory plunging wave and along a fully mobile medium sand breaker bar. Data fromthe same experiment were used before to study wave breaking effects on wave bottomboundary layer hydrodynamics (Chapter 2) and on suspension processes (Chapter 3). Thepresent study particularly addresses four matters: (i) the potential effects of wave breaking onsheet flow dynamics, which are measured using a novel conductivity based concentrationmeasurement system (CCM+; van der Zanden et al., 2015a); (ii) the cross shore variation inbedload transport rates in relation to the hydrodynamic forcing and to the suspendedtransport; (iii) the contributions of net bedload and suspended sand transport to themorphological evolution of the breaker bar; (iv) grain size sorting of suspended sediment andof the sand bed.
The paper is organized as follows. Section 4.2 explains the instrumental set up and datatreatment steps. Section 4.3 presents the measured bed evolution and the main flowparameters in the experiment. Sheet flow observations and estimated bedload transport ratesare presented in Section 4.4. Section 4.5 presents and discusses the cross shore varyingcontributions of suspended and bedload transport to breaker bar morphodynamics. Section4.6 presents measurements of grain sorting in suspended sediment and along the cross shorebed profile. Results are discussed in Section 4.7; Section 4.8 presents the main conclusions.
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4.2 Experimental description
4.2.1 Facility and test conditions
The experiments were conducted in the large scale CIEM wave flume at the UniversitatPolitècnica de Catalunya (UPC) in Barcelona. The flume is 100 m long, 3 m wide and 4.5 mdeep, and is equipped with a wedge type wave paddle. Figure 4.1 shows the experimental setup and bed profile for the present study. Cross shore coordinate x is defined positivelytowards the beach, with x = 0 at the toe of the wave paddle. Vertical coordinate z is definedpositively upwards with z = 0 at the still water level (SWL). is used for vertical coordinatepositive upwards from the local bed level.
The bed profile consisted of medium grained sand with sediment characteristics as detailedin Section 4.2.4. The reference bed profile consisted of a bar trough configuration (Figure 4.1a,black line) that was produced by 105 minutes of wave action over an initially flat horizontaltest section (Chapter 2). The initial profile is roughly divided into an offshore slope of thebreaker bar (x = 35.0 to 54.8 m; steepness tan( ) = 0.10), followed by a steeper shoreward facingbar slope (x = 54.8 to 57.5 m; –tan( ) = 0.21), and a mildly sloping bed shoreward from the bartrough (x = 57.5 to 68.0 m; tan( ) = 0.01). The profile shoreward of the mobile test section (x >68.0 m) followed a slope tan( ) = 0.13, was fixed with geotextile, and was covered withdissipative concrete slabs that promoted wave energy dissipation.
The experiments involved monochromatic waves with wave period T = 4 s and wave heightH0 = 0.85 m at water depth h0 = 2.55 m near the wave paddle. These conditions correspond toa surf similarity parameter 0 = 0.54 (where 0= tan ( )/ H0/L0, tan( ) is the offshore bar slopeand L0 is the deep water wave length), which, matching the classification of Battjes (1974),resulted in plunging breaking waves at the top of the breaker bar.
Following Svendsen et al. (1978), we define the ‘break point’ as the location where the wavestarts to overturn (at x = 53.0 m). The ‘plunge point’ (x = 55.5 m) is the location where theplunging jet strikes the water surface (Peregrine, 1983). The ‘splash point’ (x = 58.5 m) is thelocation where the water mass pushed up by the plunging jet strikes the water surface a secondtime, and where a surf bore starts to develop (Smith and Kraus, 1991). These regions are usedto define the shoaling zone (up to break point; x 53.0 m), the breaking region (between breakand splash points; 53.0 < x < 58.5 m) and the inner surf zone (shoreward from splash point; x >58.5 m) following Svendsen et al. (1978). Figure 4.1b includes these points and regions forreference.
4.2.2 Instrumentation
Near bed and outer flow hydrodynamics and suspended sediment concentrations weremeasured with a vertical array of acoustic instruments deployed from a custom built mobileframe (Figure 4.2). This frame consisted of stainless steel tubing with 30 mm diameter and wasdesigned such that it would have minimum flow perturbation while being sufficiently stiff towithstand wave impact. The frame was mounted to a horizontally mobile trolley on top of theflume, and could be vertically positioned with sub mm accuracy using a spindle. The mobileframe set up enabled measurements at various cross shore positions, while maintaining an
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approximately equal elevation of the instrument array with respect to the bed at the start ofeach run.
Figure 4.1. Experimental set up and measurement locations. (a) Reference bed profile (black line) andfixed beach (grey line), plus locations of resistive wave gauges (RWGs, vertical black lines); (b)Measurement positions of ADVs (star symbols), mobile frame Pressure Transducers (PT, white
squares), wall deployed PTs (black squares), Transverse Suction System nozzles (TSS, black dots),Optical Backscatter Sensor (black crosses), and measuring windows of mobile frame Acoustic
Concentration and Velocity Profiler (ACVP, grey boxes).
The velocity is measured at outer flow elevations using three acoustic Doppler velocimeters(ADVs) and near the bed with an acoustic concentration and velocity profiler (ACVP), alldeployed from the mobile frame. Near bed sand concentrations are obtained by inverting thereflected ACVP measured acoustic intensity signal to sand concentration using calibrationmeasurements by a six nozzle Transverse Suction System (TSS) and an optical backscattersensor (OBS). More details on the velocity and suspended sediment concentrationmeasurements are found in Chapter 2 and Chapter 3.
Time varying sediment concentrations in the sheet flow layer were measured using twoConductivity based Concentration Measurement (CCM+) tanks (Figure 4.1b). These tankswere located at the bar crest at x = 53.0 m (at break point where wave starts to overturn) andat x = 54.5 m (between break point and plunge point). Over the high sand concentrations (100– 1600 kg/m3) in the sheet flow layer, the measured conductivity of a water sand mixture is alinear function of sand concentration, which makes the conductivity based measuringprinciple highly suitable for studying sheet flow dynamics (Ribberink and Al Salem, 1995;Dohmen Janssen and Hanes, 2002; Lanckriet et al., 2013). The CCM+ tanks in the present studyare equipped with one single conductivity probe plus a combined double probe (for tank 1),or with one single probe (tank 2), and sample with a 1000 Hz data rate. The two sensors of the
0 10 20 30 40 50 60 70 80
z (m
)
-2
-1
0 SWL
RWGs
h0=2.55 mht=1.35 m
x
H=0.85 m, T=4 s(a)
x (m)50 55 60 65
z (m
)
-1.5
-1
-0.5
0
0.5(outer) breaking regionshoaling region inner surf zone
ACVP
ADV
PT (mob.)
TSS
PT (wall)
ζ
zSWL break point plunge point splash point
CCM+
tank 1CCM+
tank 2
(b)
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combined probe of tank 1 (Figure 4.2 inset) are spaced 1.5 cm in cross shore direction and canbe used to estimate particle velocities in the sheet flow layer by cross correlating both sensors’signals (see McLean et al., 2001). The probes penetrate the sheet flow layer from below tominimize flow disturbance.
Figure 4.2.Mobile measuring frame and instrumentation. Instrumentation includes three acousticDoppler velocimeters (ADVs, blue solid circles), one pressure transducer (PT, yellow square), a six
nozzle transverse suction system (TSS, yellow circles), an (black dashed circle) and an acousticconcentration and velocity profiler (ACVP, blue rectangle). Inset shows close up of CCM+ tank 1
sensors and another ACVP system, deployed from the sidewall. Note that the CCM+ sensors are raisedhere above the bed; during the experiment the tops of the sensors are within +/ 1 cm from the bed.
The tanks are equipped with a bed level tracking system that enables automatic repositioningof the probes with sub mm accuracy and which is fully described in van der Zanden et al.(2015a). In tracking mode, the probes track the continuous elevation of the bed water interface,hence they measure the bed evolution at wave averaged or longer time scales. Alternatively,the user can select to use the probes to measure sheet flow concentrations at a fixed absoluteelevation (i.e. no tracking). In the present study, both types of measurements were alternatedfor fixed intervals of 60 s: sheet flow concentration measurements were obtained at elevationsof 2, +0, and +4 mm with respect to the bed; after each of these intervals, the probes wererepositioned to the local bed level by activating the tracking system. Through this procedure,concentrations were sampled over the complete sheet flow layer while at the same time thebed level was measured with +/– 1 mm accuracy.
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A six nozzle Transverse Suction System (TSS) was used to collect samples of suspendedsediment at 0.02, 0.04, 0.10, 0.18, 0.31 and 0.53 m (see Chapter 3 for more details). Thecollected samples were dry weighted and sealed. The grain size characteristics weredetermined at the University of Aberdeen using a Beckman Coulter LS 13 320 laser diffractionparticle sizer (specifications found in the user manual: Beckman Coulter Inc, 2008). Previousexperience using this particle sizer indicated a minimum amount of 2.5 g sand (correspondingto obscuration > 5%) to be required for a reliable estimate of the size distribution. Thisminimum amount was reached for all TSS samples, except for some of the samples obtainedat the furthest offshore location (x = 51.0 m) or at elevations above wave trough level. For thesecombinations of locations/nozzles, samples of different runs but for the same nozzle and crossshore location were combined to obtain the minimum amount of sand.
The water surface was measured with a combination of resistive wave gauges (RWGs) in theshoaling zone and pressure transducers (PTs) in the breaking and inner surf zone. Bed profilemeasurements were obtained at 2 cm cross shore resolution along two transects, at lateraldistances of 0.1 and 0.7 m with respect to the flume’s centerline, using echo sounders deployedfrom a second mobile trolley. The echo sounders had an estimated accuracy of +/– 1 cm andthe mean of both sensors is used to study the bed profile evolution and net sediment transportrates.
4.2.3 Measurement procedure
One experiment consisted of 90 minutes of waves, divided over six 15 minute runs, duringwhich the bed profile evolved. The bed profile was measured prior to the first run and afterevery 2nd run, i.e. at t = 0, 30, 60 and 90 minutes. After the sixth run, the flume was drained.The reference bed profile, drawn as template on the flume wall, was then restored by shovelingback transported sand and flattening any bed forms that were generated. Each experiment wasrepeated 12 times, with the mobile measuring frame moved to a new location for eachexperiment. The bed profile evolution and hydrodynamics were very similar for eachexperiment (Chapter 2) and the adopted procedure resulted in a high spatial coverage ofvelocity and concentration measurements (Figure 4.1b).
Sediment samples of the bed were taken at 12 cross shore locations at the start of the campaign(corresponding to horizontal test section), after the initial start up stage (corresponding toreference bed level and t = 0 min.) and at the end of the final experimental repeat (t = 90 min.).Bed samples were taken at each cross shore location by carefully scraping off the top layer (1to 2 cm) of sediment at three positions separated in longshore direction. In the inner surf zone,in occurrence of bed forms, the samples were taken over a complete ripple. When restoringthe profile, the sediment was reshuffled by bringing sediment from the shoaling to the innersurf zone and vice versa.
4.2.4 Sediment characteristics
Figure 4.3 shows the cumulative grain size distribution measured with the laser diffractionparticle sizer for one of the bed samples at the start of the campaign. The accordingly obtained
Chapter 4
108
median sediment diameter (D50) is 0.29 mm. This is somewhat higher than values of 0.25 mmfound for the exact same sediment by independent sieving tests at the CIEM lab and by sievingtests by the sediment supplier. This difference is explained by sand grains not being perfectspheres: the particle sizer measures an equivalent ‘perfect sphere’ diameter; sieving yields thediameter of the smallest cross sectional area of a non spherical grain (Eshel et al., 2004). Thedegree of uniformity is quantified through the geometric method of moments g (Blott andPye, 2001). With a measured g = 1.36 and following Blott and Pye (2001), the sand is classified‘well sorted’. The sand grains had a measured mean settling velocity of 0.034 m/s.
Figure 4.3: Cumulative grain size distribution of sediment in bed at start of experiment (as obtainedwith laser diffraction particle sizer).
4.2.5 Data treatment
Data treatment steps related to hydrodynamics and suspended sediment concentrations andfluxes is described extensively in Chapter 2 and 3. These steps are only briefly repeated here.
Visual observations and measurements revealed that a hydrodynamic equilibrium establishedfor each run after approximately 5 minutes. Therefore, only the last 10 minutes of data fromeach run (corresponding to about 150 wave cycles) were used for analysis. Flume seichinginduced a standing wave with an approximately 45 s period. The seiching wave could beidentified in auto spectra of water surface and horizontal velocities, but not in bed level andsuspended sediment concentrations. Hence, its effect on sediment processes is considerednegligible. The standing wave was removed from water surface and velocity time series byapplying a high pass filter with a cut off frequency of 0.125 Hz (half the primary wavefrequency).
The phase averaged value of a variable are annotated with angle brackets and are calculatedover Nwave repetitions as
< > t =1N
(t+ n – 1 T)N
n=1
(4.1).
Reference zero up crossings, required to phase reference each wave cycle prior to phaseaveraging, were based on water surface measurements at x = 47.6 m. Data were phase
D (mm)0 0.1 0.2 0.3 0.4 0.5 0.6
Cum
ulat
ive
frac
tion
0
0.1
0.5
0.9
1
D10 = 0.19 mm
D50 = 0.29 mm
D90 = 0.42 mm
Bedload processes and breaker bar morphodynamics
109
referenced such that t/T=0 corresponds to maximum surface elevation (wave crest) at thebeginning of the test section (x = 50.0 m). Phase averaged horizontal velocities <u> consist of atime averaged component , i.e.
u =1T
<u t >dtT
0
(4.2)
and a periodic component = <u> – . Root mean squared is denoted rms.
The CCM+ tanks were at fixed cross shore locations during the experiment. Measurementswere phase averaged for each 15 min. stage of bar development over all 12 experimentalrepeats, resulting in a large number of wave repetitions (N>1000). For the time varying sheetflow concentration measurements C( ,t), =0 is defined as the bed level during the zero downcrossing of the wave when the bed is considered to be at rest (‘immobile bed level’). Intrawave bed level fluctuations are preserved in phase averaged results. C( ,t) measurementswere bin averaged, where the bin class was based on the relative elevation and the binresolution = 0.25 mm. For each wave phase and elevation bin, <C( i,t)> is calculated as themedian of concentration measurements at i – /2 < i < i + /2.
For calculating sand particle velocities in the sheet flow layer, the concentration time series ofthe two sensors of the combined probe were first high pass filtered (fcutoff = 1 Hz). The crosscorrelation of the two sensors’ signals was calculated over regular time intervals t = 0.1 s.Each wave cycle was assigned a concentration bin class (bin resolution C = 0.1 m3/m3) basedon wave averaged concentration. The cross correlation output was then averaged for each Cbin class and each wave phase t/T. The bin averaged cross correlation is used to quantify thetime lag between both signals, which with known distance between the sensors is translatedinto a particle velocity (see further McLean et al., 2001; van der Zanden et al., 2015a).
Volumetric total sediment transport rates qtot, due to contributions by both bedload andsuspended load, can be obtained from measured bed profile measurements zbed by solving theExner equation:
qtot(x) = qtot x x + x 1 0zbedt
(4.3)
Here, 0 is the sand porosity (0.6 if loosely packed), x is the horizontal resolution of zbedmeasurements (=0.02 m) and t is the time interval between two consecutive profilemeasurements (30 min.). Equation 4.3 can be solved if qtot is known at one x location. With qtot= 0 at the left hand (i.e. x = 35 m) and right hand boundary (x = 68 m) of the mobile test section,qtot can be solved iteratively by starting from either the left or the right hand side of the profile.This yields two estimates of qtot, annotated qlhs and qrhs respectively. The estimates qlhs and qrhsare likely different due to variations in the horizontally integrated volume of the two profilemeasurements used to quantify zbed. These variations can be attributed to sampling errors ofthe acoustic sensors, 3D bed forms, variations in packing density and porosity, and nonuniformity of the bed profile (e.g. Baldock et al., 2011). Depending on distance to eachhorizontal boundary of the test section, qlhs or qrhs is considered more accurate. Therefore, thevolumetric total transport rate qtot used in the present study was calculated as the weightedaverage of both estimates:
Chapter 4
110
qtot(x) =xend xxend x0
qlhs(x) +x x0xend x0
qrhs(x) (4.4)
with x0 = 35 m and xend = 68 m being the left and right hand boundary of the mobile bed profile,respectively. The transport rate qtot(x) was calculated for each experimental repeat and wasthen averaged over all repeats.
4.3 Hydrodynamics and bed profile evolution
This section presents an overview of the main hydrodynamics and the bed profile evolution.The reader is referred to Chapter 2 for a more detailed description of the near bedhydrodynamics (including turbulence) in the present experiment and to Van der A et al.(submitted) for an extensive analysis of the outer flow hydrodynamics for an accompanyingrigid bed experiment with the same bed profile and wave conditions.
4.3.1 Hydrodynamics
Table 4.1 presents an overview of the main hydrodynamic parameters at the 12 measurementlocations. Figure 4.3a shows the wave height H and time averaged water level . The waveheight reduces by 50% between the break point (around x = 53.0 m) and splash point (x = 58.5m). Water levels show a set down at the shoaling locations and set up at the inner surf zone.Figure 4.3b shows time averaged velocity and maximum onshore and offshore horizontalvelocity <u>max and <u>min. These values are measured at the wave bottom boundary layer(WBL) overshoot elevation ( 0.02 m) and are averaged over the complete experiment (t =0 – 90 min., i.e. over six runs). Along the offshore slope up to the bar crest (x=51.0–55.0 m),<u>max and <u>min remain roughly constant. Time averaged velocity magnitudes are lowest atx = 51.0 m and increase towards the bar crest. The skewness and asymmetry of (Table 4.1)show that the intra wave shape of changes significantly along the offshore slope. Mostnotable is the large asymmetry at x = 53.0 m at the onset of breaking wave overturning. Alongthe shoreward facing bar slope (x = 55.5 to 58.0 m), the combination of decreasing H andincreasing h leads to a substantial decrease in orbital velocity amplitude while at the same timethe magnitudes of offshore directed time averaged velocity (undertow) increases. Undertowvelocity magnitudes decrease in the inner surf zone (x > 58.5 m).
Turbulent kinetic energy (TKE) is calculated through a Reynolds decomposition of the velocitytime series (Chapter 2). Figure 4.3c shows the time averaged TKE (k) at outer flow elevationand close to the bed. The latter, kb, is defined here as the maximum kmeasured inside the WBL.Turbulence production by wave breaking leads to large magnitudes of outer flow k near theplunge point at x = 55.5 m. k decreases towards the bed at most locations, which indicates thatwave breaking is the primary source of turbulence. Breaking generated turbulence is advectedto offshore locations while gradually dissipating, and consequently, k decreases from thebreaking zone in the offshore direction (from x = 55.5 to 51.0 m). Turbulent kinetic energyinside the WBL (kb) follows a similar cross shore pattern as outer flow k, i.e. it increases by anorder of magnitude between the shoaling zone at x = 51.0 m to the breaking region at x = 56.0m. This increase occurs in spite of a decrease in <u>max and <u>min, which suggests that theincrease in kb is due to the invasion of breaking generated turbulence into the WBL. Further
Bedload processes and breaker bar morphodynamics
111
shoreward, kb decreases above the bar trough (around x = 58.0 m) and increases graduallythroughout the inner surf zone (x > 58.5 m) due to the presence of sand ripples.
Table 4.1. Hydrodynamic and bed parameters at each measurement location: water depths (h); waveheights (H); ADV measured velocity statistics at =0.11 m, with maximum onshore and offshore
phase averaged horizontal velocity, semi excursion length (a = 2T rms/2 ), velocity skewness (Sk(u) =u3/urms3), velocity asymmetry (Asy(u) = – (u)3/urms3, where marks Hilbert transform (e.g. Ruessink
et al., 2011)), local bed slope tan( ) = dzbed/dx at start (t=0 min.) and end (t=90 min.) of experiment.Hydrodynamic parameters are measured during the first run of each experimental repeat (t = 0 15
min.).
x(m)
h(m)
H(m) (m/s)
<u>max(m/s)
<u>min(m/s)
a (m) Sk(u) Asy(u)tan( ),t=0
min.
tan( ),t=90min.
51.0 1.10 0.79 0.13 1.04 0.83 0.54 0.61 0.68 0.08 0.1253.0 0.97 0.74 0.22 0.80 0.94 0.48 0.44 1.01 0.06 0.1254.5 0.88 0.64 0.19 0.84 0.85 0.47 0.50 0.82 0.04 0.0655.0 0.88 0.60 0.24 0.78 0.90 0.47 0.48 0.76 0.10 0.0355.5 0.97 0.51 0.23 0.57 0.83 0.39 0.36 0.75 0.22 0.1256.0 1.10 0.50 0.30 0.25 0.82 0.31 0.06 0.77 0.20 0.4556.5 1.19 0.53 0.51 0.05 0.83 0.25 0.67 0.76 0.18 0.5157.0 1.24 0.48 0.54 0.02 0.78 0.23 0.95 0.58 0.08 0.3558.0 1.28 0.47 0.46 0.01 0.71 0.21 0.82 0.79 0.02 0.1159.0 1.28 0.43 0.36 0.13 0.71 0.23 0.39 0.88 0.02 0.1660.0 1.26 0.42 0.36 0.17 0.66 0.24 0.67 0.68 0.03 0.0263.0 1.26 0.41 0.34 0.19 0.58 0.23 0.79 0.45 0.01 0.01
4.3.2 Bed profile evolution and net total transport
Figure 4.4a shows the bed profile evolution. The bar crest grows and migrates slightly onshoreduring the experiment. This leads to an increase in the bar’s offshore slope from tan( )=0.10 to0.13 and an increase in the surf similarity parameter 0 from 0.54 to 0.68. At the same time thebar trough deepens, resulting in a steepening of the shoreward slope of the breaker bar fromtan( ) = –0.21 to –0.47. At t=90 minutes, this slope approaches the natural angle of repose(tan( ) 0.5 to 0.7) for sandy materials (Nielsen, 1992). Table 4.1 includes the local bed slopeat the start and end of the experiment for each measurement location.
Bed forms were observed after draining the flume. The bed was flat in the shoaling region andat the bar crest (x = 48.0 to 55.5 m), indicating bedload transport in the sheet flow regime.Quasi 2D bed forms (quasi uniform in longshore direction) were identified along theshoreward slope of the bar (x = 55.5 to 57.0 m), where they migrated progressively offshore.Shoreward facing lunate shaped bed forms were formed at the bar trough (x = 57.0 to 59.0 m).At the inner surf zone a gradual transition to quasi 2D bed features occurs (from x = 59.0 to62.0 m). Further shoreward these features became increasingly irregular while their wavelength reduced, resulting in 3D sand ripples (x = 62.0 m to 68.0 m). In the inner surf zone (x >58.5 m) bed form lengths were of similar magnitude as the orbital semi excursion length a. Thebed forms in the breaking region have lengths that exceed a by a factor 2 to 5.
Chapter 4
112
Figure 4.4. (a) Bed profile evolution (solid lines, with each line representing the mean value over allexperimental days), and water levels for t=0–15 min. (dots and dashed lines depict time averaged andenvelope, respectively); (b) ACVP measured horizontal velocity at the WBL overshoot elevation = ,for t= 0–90 min., time averaged (circles) and maximum phase averaged onshore and offshore velocity
(dots and dashed line); (c) Turbulent kinetic energy, mean values over experiment (t=0–90 min.) atouter flow elevation = 0.38 m (measured with ADV, solid line + circles) and inside the WBL
(measured with ACVP, dashed line + squares).
The bar growth can be explained by accumulation of primarily onshore directed totaltransport at shoaling locations and offshore directed transport in the breaking and inner surfzone (Figure 4.5). The reversal of transport direction occurs near the breaker bar crest (x = 54.5m), about 1 m offshore from the plunge point. The sharp gradients dqtot/dx at the breakingregion are indicative of a strong cross shore non uniformity in sand transport processes. Notethat qtot is not constant throughout the experiment; instead, the magnitudes of onshore andoffshore qtot decrease as the breaker bar evolves towards a semi equilibrium state (Van derZanden et al., 2015b). This morphologic feedback of profile evolution on time evolvingtransport rates is not further considered in the present study.
z (m
)
-1.5
-1
-0.5
0
0.5
SWL
ηcrest
η
ηtrough
(a)
plunge point
t=0 min.t=30 min.t=60 min.t=90 min.
u(δ)
(m/s
)
-1-0.5
00.5
1〈u〉max
u〈u〉min
(b)
x (m)50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
k (m
2 /s2 )
0
0.01
0.02
0.03(c)
k(ζ = 0.38 m)kb
Bedload processes and breaker bar morphodynamics
113
Figure 4.5. (a) Total transport during experiment (t=0–90 min.) obtained through Equation 4.4, meanvalues (dashed) +/ 95% confidence interval (dotted) over all experimental repeats; (b) Initial (solid)
and final (dashed) bed profile. The grey shading marks the region of net accretion.
4.4 Bedload transport processes
This section first presents and discusses sheet flow measurements (Sections 4.4.1 to 4.4.3)which are compared with oscillatory sheet flow observations in tunnels and under nonbreaking waves to assess the effects of wave breaking. Next, Section 4.4.4 presents the crossshore varying bedload transport rates and relates these to the near bed hydrodynamics.
4.4.1 Sheet flow layer concentrations
The sheet flow layer behavior is explored using CCM+ measurements at two locations near thebreaker bar crest, i.e. at x = 53.0 m (below break point) and x = 54.5 m (between break pointand plunge point). Figure 4.6c,d shows phase averaged concentrations <C( ,t)>, bin averagedfor vertical elevations with bin resolution = 0.25 mm and based on a minimum of threewave repetitions. Due to the chosen settings for probe repositioning during acquisition, thisminimum was not obtained for each bin class (which explains the data gaps e.g. at 2 mm,Figure 4.6c). Figure 4.6e,f also shows concentration time series, but for these panels Cwas binaveraged based on the wave averaged concentration. The latter approach preserves thetemporal variation in C that occurs at intra wave time scale and it has been adoptedthroughout many sheet flow studies (Ribberink and Al Salem, 1994; O Donoghue and Wright,2004a; Schretlen, 2012). This approach is especially useful to study phase lags between theupper sheet flow layer (region above the ‘immobile bed level’, i.e. > 0, with typicalconcentrations lower than 0.3 m3/m3) and the erosion layer ( < 0, C>0.3 m3/m3).
Despite sheet flow layers being rather thin, of O(mm), the CCM+ manages to resolve the timevarying concentrations adequately. This is partly ascribed to the new automatic probe
40 45 50 60 65 70
q tot (m
3 /ms)
×10-5-5
0
5Breaking region
(a)
x (m)40 45 50 55 60 65 70
z (m
)
-2
-1.5
-1
-0.5
0accretion erosionerosion(b)
0 min.90 min.
Chapter 4
114
Figure 4.6. Time series of phase averaged CCM+ measurements at x=53.0 m (left) and x=54.5 m (right),for final stage of bar development (t=75–90 min). (a,b) ACVP measured velocities at = . (c,d)
Concentration contour, with dashed black lines marking bottom and top of sheet flow layer (see text);(e,f) Concentration time series, obtained through bin averaging, at 7 different relative elevations.
These elevations are indicated in the panel and have a typical standard deviation of +/ 1 mm; (g,h)Sheet flow layer thickness.
repositioning system, which allows measurements of the time varying relative bed level withhigher accuracy than previous versions of the CCM system. At both CCM+ locations, instancesof peak offshore and onshore velocities lead to a quasi instantaneous concentration decreasein the erosion layer (C<0.3 m3/m3) and a simultaneous increase in the upper sheet flow layer(C<0.3 m3/m3). The erosion layer responds layer by layer to velocity forcing, i.e. concentrationsat elevations deeper in the erosion layer ( 2 to 1 mm) respond slightly later thanconcentrations near = 0. Hence, no evidence of plug flow (Sleath, 1999) is found, despiteSleath parameters estimated from flow acceleration reach magnitudes (up to 0.3) that are wellabove proposed critical thresholds for plug flow (Foster et al., 2006). The short increase inupper sheet flow layer sediment concentration around flow reversal (t/T = 0.17) at x = 53.0 mhas also been observed in oscillatory sheet flow conditions and may relate to shear instabilitiesaround flow reversal (Ribberink and Al Salem, 1995; O’Donoghue and Wright, 2004a).
Bedload processes and breaker bar morphodynamics
115
4.4.2 Sheet flow layer thickness
The time varying sheet flow layer s is the difference between the intra wave time varyingbottom (i.e. erosion depth, with <C> = 0.60 m3/m3) and the top of the sheet flow layer (i.e. theelevation with <C> = 0.08 m3/m3; Dohmen Janssen and Hanes, 2002). These elevations wereestablished by fitting the empirical function of O Donoghue and Wright (2004a) for verticalsheet flow concentration profiles through the time varying concentration measurements (theapproach is described more extensively in Van der Zanden et al., 2015a). The function fittedwell through the measurements (r2 > 0.9 for each profile). Figure 4.6c,d includes the timevarying erosion depth and top of the sheet flow layer and Figure 4.6g,h shows the intra wavesheet flow thickness s.
The sheet flow thickness shows similar phase behavior as the near bed velocity magnitude,which again illustrates the quasi instantaneous response of sheet flow pick up to near bedvelocity. At x = 53.0 m, s returns to near zero during the crest to trough flow reversal, whichindicates that most of the sediment that was entrained from the bed to the upper sheet flowlayer during the crest phase, has settled down once the flow reverses. At x = 54.5 m, s is about1.5 mm (i.e. non zero) during the crest to trough flow reversal, possibly due to the significantdeposition rate (about –0.2 kg/m2s) of suspended sediment at this location during this phaseof the wave cycle (Chapter 3).
At both locations, the non zero s around trough to crest flow reversal indicates that a majorfraction of sediment particles that have been entrained during the trough phase has not fullysettled as the crest phase begins. This lagging of sheet flow layer concentration is caused bythe relatively short time interval between maximum offshore and maximum onshore velocitiesin highly acceleration skewed flows (Watanabe and Sato, 2004; Van der A et al., 2009; Ruessinket al., 2011). Maximum sheet flow thicknesses at both locations are higher during the crest thanduring the trough phase. This can be attributed to skewness in near bed velocities and inaccelerations, both leading to higher bed shear stress during the crest phase. Surprisingly, s
during the trough phase reaches larger values at x = 54.5 m than at x = 53.0 m, despite troughphase velocity magnitudes being significantly higher at x = 53.0 m.
To assess whether wave breaking affects the sheet flow layer thickness, s is quantitativelycompared with predictions by two empirical formulations for maximum s that have beenproposed on the basis of detailed laboratory measurements using well sorted sand and regularoscillatory and wave conditions: firstly, the formulation by Ribberink et al. (2008) based onoscillatory tunnel data:
s/D50 = 10.6 (4.5),
and secondly, Schretlen’s (2012) formulation based on uniform non breaking wavesmeasurements:
s/D50 = 13.1 0.7 (4.6).
The Shields parameter is the non dimensional bed shear by phase averaged velocities, i.e.= b/( s – )gD50, with s (=2650 kg/m3) and (=1000 kg/m3) being the densities of sedimentparticles and water, respectively, and g (=9.81 m/s2) is the gravitational acceleration. The bed
Chapter 4
116
shear stress b is estimated based on the horizontal velocity at = through b = 0.5fwcu( )2. Themethodology described by Ribberink (1998) is applied to calculate the wave plus currentfriction factor fwc as a linear combination of the wave friction factor fw and the current frictionfactor fc. The wave friction factor fw is calculated based on the widely used formulation bySwart (1974), modified to account for acceleration skewness (da Silva et al., 2006; van der A etal., 2013):
fw=0.00251exp 5.21 2Ta0.49 a
ksw
0.19(4.7)
with ksw being the bed roughness, calculated iteratively as a function of the Shields parameter(see Ribberink, 1998), and Ta is the relative time duration of accelerating flow within a halfcycle. In the present study, Ta equals approximately 0.3 during the crest phase and 0.6 duringthe trough phase. This yields friction factors fw that are approximately 30% higher for the crestphase and 6% lower for the trough phase compared to fw calculated without accelerationskewness correction (i.e. Ta = 0.5 in Equation 4.7). The maximum bed shear max and sheet flowthickness s are derived per half cycle and for each 15 minute stage of bar development,yielding a total of 24 data points.
Figure 4.7 shows measured s versus max. The predictions by Equations 4.5 and 4.6 describethe measured data reasonably well. This suggests that s in the present breaking waveconditions is consistent with previous observations in oscillatory flow tunnel and nonbreaking wave conditions. Apparently, the effects of the sloping bed, the presence of breakinggenerated turbulence in the WBL, and of horizontal sediment advection, generally have minoreffects on the sheet flow layer thickness. An exception occurs at x = 54.5 m, where trough phases exceeds predictions of Equation 4.5 and Equation 4.6 by 75% and 35%, respectively.
Near bed (breaking generated) TKE could be postulated as a factor contributing to increaseds (e.g. Lanckriet and Puleo, 2015). At this location, <kb> for both half cycles is much higher
than at the reference shoaling zone location (x = 51.0 m) where TKE is predominantly bedgenerated (Chapter 2). Consequently, the presence of breaking generated turbulence wouldexpectedly lead to similar qualitative effects on s during both half cycles. Since s exceedsempirical predictions only during the trough phase, it is not likely that the increased s ispurely due to the presence of breaking generated turbulence. The increase in s may also beexplained by non uniform advection of sediment along the bed. It was shown for the presentstudy that suspended sediment entrained under the plunge point is carried offshore toshoaling locations by undertow and periodic velocities during the trough phase, leading to asignificant horizontal influx of sediment at x = 54.5 m between t/T = 0 and 0.3 (Chapter 3). It islikely that this cross shore influx of sediment is not limited to suspended sediment, but alsoaffects sediment concentrations in the sheet flow layer during the same time interval (seeFigure 4.6d,f). This means that sheet flow concentrations are not fully controlled by localhydrodynamic forcing but instead, are affected by the intra wave cross shore sedimentadvection.
The empirical formulations in Equations 4.5 and 4.6 have never been validated for progressingasymmetric waves inducing strong near bed acceleration skewness. Due to the scatter of thedata and the limited range of hydrodynamic forcing covered in the present study, it cannot be
Bedload processes and breaker bar morphodynamics
117
concluded whether the relation between s and in Figure 4.7 is linear. Although theformulation of Schretlen (2012) performs slightly better than the one of Ribberink et al. (2008),we remark that neither of the two original formulations were developed for accelerationskewed flows. If the acceleration correction is dismissed (i.e. by setting Ta = 0.5 in Equation4.7), the estimated crest phase decreases while the trough phase increases. In that case, ascan be concluded from Figure 4.7, the data points approach the Ribberink et al. (2008)predictions more closely but move away from Schretlen’s (2012) predictions.
Figure 4.7. Maximum sheet flow layer thickness versus maximum Shields stress per wave half cycle.Also included are empirical relations proposed by Ribberink et al., 2008 (solid line) and Schretlen,
2012 (dashed line).
4.4.3 Sheet flow particle velocities and fluxes
Particle velocities up( ) across the sheet flow layer were estimated for CCM+ tank 1 at x = 54.5m through cross correlation of concentration measurements by two probes aligned in wavedirection (see Section 4.2.5). Inherent to the applied CCM cross correlation technique is thatreliable estimates of particle velocities can only be obtained when the sheet flow layer is welldeveloped (c.f. Dohmen Janssen and Hanes, 2002). Because the sheet flow layer in the presentstudy is rather thin, up could only be measured around instances of maximumonshore/offshore velocity. We focus here on the final run (t = 75–90 minutes) when near bedvelocities were highest and the best measurements of up are obtained.
Figure 4.8a shows phase averaged particle velocities for t = 75–90 min. Reliable estimates of upwere obtained for phases with s roughly exceeding 4 mm. The particle velocities are in phasewith near bed water velocity and increase in magnitude with distance away from the bed.Magnitudes of up are typically about 40 70% of the near bed flow velocity at = . Theserelative magnitudes and the vertical structure are both consistent with previous observationsof oscillatory sheet flows (e.g. McLean et al., 2001; Dohmen Janssen and Hanes, 2002; DohmenJanssen and Hanes, 2005).
The particle velocities were multiplied with corresponding concentrations to obtain horizontalsediment fluxes x (Figure 4.8b). Highest sediment fluxes are found deep in the erosion layerbecause concentrations increase rapidly towards the bed while the vertical decay of velocitiesis much more gradual. Note that flux magnitudes in the sheet flow layer (100–500 kg/m2s) are
θmax
0 1 2 3 4 5
δ s/D50
0
10
20
30
40
50δs/D50=10.6θ
r2=0.23
δs/D50=13.1θ 0.7
r2=0.49
x=53.0, crestx=53.0, troughx=54.5, crestx=54.5, troughRibberink et al., 2008Schretlen, 2012
Chapter 4
118
orders of magnitude higher than horizontal suspended sediment fluxes measured just abovethe WBL at the same location (1–10 kg/m2s) (Chapter 3).
Figure 4.8. Sheet flow particle velocities and sediment fluxes measured with CCM+ at x=54.5 m, for t =75 90 min. (a) ACVP measured velocities at = (line) and particle velocities measured with CCM+ foreight concentration bin classes (circles, with color coding indicating the volumetric concentration, see
color bar in panel b); (b) Flux measurements, as product of CCM+ measured particle velocities andconcentrations; (c) Time varying depth integrated transport over the sheet flow layer.
The time varying total transport qsfl(t) was estimated as the depth integrated product ofmeasured concentrations C and estimated particle velocities up over the sheet flow layer, i.e.from the erosion depth ze to the top of the upper sheet flow layer zt:
qsfl(t) = up( t)C( t)d
zt
ze
(4.8)
The full up( ,t) profile was obtained by fitting an empirical power law distribution, proposedby Sumer et al. (1996), through the measurements:
up( ) = m n (4.9),
with m and n as fitting parameters. Equation 9 was log fitted for each phase with a minimumof three up( ) measurements and accepted only if n > 0, yielding fitted up( ) profiles for 12 outof 40 wave instants with an average r2 = 0.62. The accordingly obtained velocity distributionsmay not be fully correct but are considered sufficiently accurate for estimating the magnitudeof qsfl(t).
u (m
/s)
-1
0
1(a)
φx (k
g/m
2 s)
-1000
-500
0
500
1000 C=(b) 0 0.6
t/T0 0.2 0.4 0.6 0.8 1
q sfl (k
g/m
s)
-2
-1
0
1
2(c)
Bedload processes and breaker bar morphodynamics
119
Results of qsfl(t) in Figure 4.8c show that instantaneous transport rates during the crest phaseexceed those during the trough phase with about 50%. This is consistent with s being largerduring the crest phase. Indeed, Figure 4.8b shows that sediment fluxes associated with aparticular concentration are of similar magnitude during trough and crest phase. Hence, thevertical profile of horizontal fluxes is of similar shape during both crest and trough phase, andthe larger sheet flow thickness during the crest phase leads to flux profiles that are verticallystretched and yield larger transport rates. It is further interesting to note that qsfl(t) is of O(1–2kg/ms), which is of similar magnitude as the depth integrated outer flow suspended loadtransport qs(t) at this location (approximately 2.0 (+/ 0.2) kg/ms, Chapter 3).
Averaging qsfl(t) over the wave period yields a rough approximation of the time averagedtransport in the sheet flow layer qsfl, excluding transport contributions around flow reversals
when up could not be measured. Estimated qsfl = 0.03 (+/ 0.1) kg/ms, i.e. the net transport over
a wave cycle is two orders of magnitude lower than the instantaneous transport rate duringthe half cycles.
4.4.4 Net bedload transport rates
The total net (i.e. wave averaged) transport rate qtot is formed by a depth integrated suspendedload (qs) and a bedload (qbed) contribution. Direct measurement of the bedload transport rate inoscillatory conditions is generally very difficult, because the transport is confined to layers ofO(sub mm) which cannot be accurately resolved by most measuring instruments. The CCM+
is one of the few instruments capable of measuring qbed in sheet flow conditions, provided thatsheet flow layers are sufficiently developed ( s > 4 mm). Most previous laboratory studiesfocusing on bedload transport rates could assume negligible suspended load transport (i.e. qbedqtot), allowing quantification of qbed from bed profile measurements (i.e. through Equation 4.3).
However, the breaking waves in the present study bring large amounts of sediment intosuspension and consequently, qs cannot be neglected. Following previous surf zone studies(Grasmeijer and Van Rijn, 1997; van der Werf et al., 2015), qbed is estimated at each location asthe difference between the total transport (Equation 4.3) and the suspended transport rates:
qbed x = qtot x qs x = qtot x u x, C x, d (4.10)crest
za
The net suspended transport rate qs was estimated in Chapter 3 as the time averaged crossshore sediment flux, depth integrated from a near bed reference elevation za that defines theboundary between the bedload layer ( <za) and the suspension layer ( <za) up to wave crestlevel crest. The reference elevation za = 0.005 m, which roughly equals the maximum elevationof the sheet flow layer across the test section. The possible sources of measurement errors forqbed are addressed in Section 4.7 (Discussion).
Figure 4.9a presents qbed across the breaker bar. The standard deviation over the sixmeasurements of qbed at each location equals 0.04 kg/ms on average, which includes thevariability due to the morphologic feedback by the bed profile evolution. The figure includesthe time averaged sheet flow layer transport measured with the CCM+, qsfl = 0.03 kg/ms. Note
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120
the wide error margins (+/ 0.1 kg/ms) of this measurement, which illustrate the difficulties ofobtaining direct measurements of bedload transport rates. At this location, Equation 4.10yields qbed = 0.07 (+/ 0.04) kg/ms, which is close to the estimated qsfl and within the latter’s error
margins. The bedload transport rates (Figure 4.9a) can be explained in terms of hydrodynamicparameters, i.e. the onshore and offshore phase averaged velocity (Figure 4.9b) and thedimensional periodic velocity skewness u 3 and the dimensional acceleration skewness –
( u )3 (where is the Hilbert transform, see e.g. Ruessink et al., 2011) (Figure 4.9c).
Figure 4.9. Bedload transport rates across the bed profile. (a) qbed, mean (red circles) plus 95%confidence interval (error bars) over six runs per location. Also included is the time averaged sheet
flow transport measured with CCM+ at x = 54.5 m for t = 75–90 min. (blue star, with error barsindicating the estimated error = +/ 0.1 kg/ms); (b) Horizontal velocity at the WBL overshoot elevation,time averaged (black circles) and maximum onshore and offshore phase averaged (dots and dashed
lines) for t = 0 90 min; (c) Dimensional velocity skewness (circles) and dimensional accelerationskewness (squares) at the WBL overshoot elevation, mean values over six runs plus 95% confidence
interval (error bars); (d) Bed profiles at start (solid) and end (dashed) of experiment.
At x = 51.0 m, qbed is positive (i.e. onshore), which is explained by the strong velocity andacceleration skewness of near bed velocities and the relatively low magnitude of timeaveraged undertow velocities (Table 4.1). Note that this location corresponds roughly to thelocation of maximum qtot as obtained from bed profile measurements (Figure 4.5). Magnitudesof qbed are similar at x = 53.0 m (below break point), where the dimensional accelerationskewness is maximum. Towards the bar crest (x = 54.5–55.0 m), qbeddecreases, which may be
q bed (k
g/m
s)
-0.1
0
0.1
0.2
plunge pointbreak point
qsfl (CCM+)
(a)
u (m
/s)
-1
0
1〈u〉max
〈u〉min
(b)
〈u〉3 ,
−H(u)3
(m3/s3)
0
0.2
0.4−H(u)3
〈u〉3
(c)
x (m)50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
z (m
)
-1.4-1.2
-1-0.8-0.6 (d)
0 min.90 min.
Bedload processes and breaker bar morphodynamics
121
caused by the horizontal influx of sediment during the wave trough phase as discussed indetail in the Discussion section (Section 4.7).
Shoreward from the plunge point and along the lee side slope of the bar, qbed increasessignificantly. Note that qbed > 0 while near bed velocities are predominantly negative. Hence,the onshore transport is likely due to the large steepness of the bar, which approaches thenatural angle of repose and induces downward (onshore) bedload transport by gravity. Thebreaker trough (x = 58.0 m) is the only location where qbed is directed offshore. This is explainedby the combination of the positive bed slope dzbed/dx and the strong offshore directedundertow velocities relative to periodic velocities. Further shoreward, at the inner surf zone (x= 59.0 – 63.0 m), qbed is again shoreward directed with magnitudes gradually approaching zero.
Figure 4.10. Scatter plot between bedload transport and near bed hydrodynamic parameters for 6 runsat 12 cross shore locations (72 data points). Explaining variables are (a) periodic velocity cubed; (b)
dimensional acceleration skewness through Hilbert transform – (u)3; (c) time averaged TKE in WBL;(d) local bed slope. Velocity variables (a b) are obtained at overshoot elevation = . Distinction ismade between measurements along offshore bar slope to bar crest (x 55.5 m; grey squares) and
breaking region from bar crest to bar trough (56.0 x<58.5 m; blue circles).
In order to obtain more insight in the parameters controlling the measured bedload transportrates, Figure 4.10 shows scatter plots of qbed versus a number of hydrodynamic parameters. Thechosen parameters are the dimensional orbital velocity skewness, u 3 (Figure 4.10a); thedimensional acceleration skewness, – ( u )3 (Figure 4.10b); the near bed turbulent kineticenergy kb (Figure 4.10c); and the local bed slope –dzbed/dx (Figure 4.10d). Distinction is madebetween two characteristic zones along the test section, i.e. the offshore slope up to the barcrest (x 55.5 m) and the breaking region covering the bar crest up to the bar trough (55.5 < x< 58.5 m). The bedload transport rates at the inner surf zone are not considered in this analysisbecause of the presence of bed forms and the associated variability in bed roughness.
〈u3〉(m3/s3)
0 0.1 0.2 0.3 0.4
q bed (k
g/m
s)
-0.1
0
0.1
0.2
0.3
0.4
Schretlen (2012)
(a)
−H(u)3(m3/s3)
0 0.2 0.4 0.6
q bed (k
g/m
s)
-0.1
0
0.1
0.2
0.3
0.4
x ≤ 55.5 m
56.0 m ≤ x < 58.5 m(b)
kb (m2/s2)0 0.01 0.02 0.03
q bed (k
g/m
s)
-0.1
0
0.1
0.2
0.3
0.4 (c)
-dzbed/dx-0.5 0 0.5
q bed (k
g/m
s)
-0.1
0
0.1
0.2
0.3
0.4 (d)
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122
For medium sand and plane bed conditions, qbed is expected to correlate positively with thedegree of orbital velocity skewness. Figure 4.10a shows qbed versus u 3 and includes a lineartrend line that was found by Schretlen (2012) for medium sand (D50 = 0.25 mm) under nonbreaking second order Stokes waves. Between x = 51.0 and 55.5 m, measured qbed in the presentstudy is of similar magnitude as the observations for non breaking waves by Schretlen (2012).The scatter in measured qbed is addressed to measuring uncertainties and to effects by otherhydrodynamic parameters than u 3. The transport rates along the shoreward bar slope(between x = 56.0 and 58.5 m) deviate clearly from the trend line, suggesting that other forcingparameters than u 3 are significant at these cross shore locations.
A positive correlation between qbed and the dimensional acceleration skewness is expected (c.f.van der A et al., 2010). Figure 4.10b shows that between x = 51.0 and 55.5 m, qbed indeedcorrelates positively with – ( u )3. However, the data points in the breaking region along theshoreward bar slope (x = 56.0 to 58.5 m) do not satisfy the overall trend.
Figure 4.10c shows the correlation between qbed and the turbulent kinetic energy inside theWBL, kb. As shown by Sumer et al. (2003) an increase in near bed TKE can lead to increased qbedmagnitudes. Figure 4.10c shows indeed a weak but positive correlation (with r2=0.13) for theobservations between x = 56.0 and 58.5 m, but no significant correlation is found for theobservations between x = 51.0 and 55.5 m.
Gravity favors downslope bedload transport, i.e. qbed is expected to correlate positively with –dzbed/dx. Figure 4.10d shows a clear positive correlation (with r2 = 0.33) between both variablesfor the observations between bar crest and bar trough (x = 56.0 to 58.5 m). This region involvesthe locations along the shoreward facing bar slope, where particularly steep local bed slopeswith a substantial effect on bedload transport are found. It is further noted that for this region,the two forcing parameters –dzbed/dx and kb are not independent (positive covariance). Becauseqbed correlates better with –dzbed/dx than with kb, it is likely that the bed slope is the primaryfactor affecting bedload transport along the shoreward bar slope.
4.5 Contributions of transport components to bar morphodynamics
4.5.1 Bedload and suspended load contributions to total transport
Figure 4.11a shows the cross shore variation in the net (i.e. wave averaged) bedload ( < za =0.005 m) and the net depth integrated suspended load ( > za) transport rates. The netsuspended load transport is further decomposed into a current related (qs,c) and wave relatedcomponent (qs,w). The latter was measured with ACVP, and was generally confined to the WBLand onshore directed (Chapter 3). Figure 4.11b shows the relative importance frel of these threecomponents to total transport, calculated as the relative contribution to the sum of the absolutevalue of individual components (e.g. for bedload, frel= |qbed| / (|qbed| + |qs,c| + |qs,w|).
At the most offshore shoaling location (x = 51.0 m), transport is almost fully (>90%) attributedto bedload. This location is hardly affected by breaking generated TKE and suspendedsediment pick up rates are low. Towards the crest of the bar, between the break point (x = 53.0m) and plunge point (x = 55.5 m), the offshore directed suspended transport gains importance
Bedload processes and breaker bar morphodynamics
123
over bedload transport, i.e. qs increases while qbed decreases. At these locations the onshoredirected wave related suspended load contribution (frel = 10–20%) is also significant.
Figure 4.11. Cross shore variation in net (wave averaged) transport rates. (a) Transport rates along testsection, split out to different components: Total net transport (dashed black line), current relatedsuspended transport (white squares), wave related transport (grey triangles), and bedload (redcircles); (b) Relative contribution of each component to total transport, calculated as individual
contribution to the sum of absolute values of the three terms (see text in Section 4.5.1); (c)Contributions by each component to bed level change (erosion/accretion), quantified throughhorizontal transport gradients divided by relative sand fraction in loosely packed bed (1 – 0):
contributions by suspended load (wave plus current related, diamonds), bedload (circles) and totaltransport (dashed line); (d) Bed profiles at t=0 and t=90 min. Values in (a c) are means over six runs,
with error bars in a b marking 95% confidence interval.
q i (m3 /m
s)
×10-4
-1
0
1
qtot
Break point Plunge point(a)
qs,c qs,w qbed
f rel
0
0.2
0.4
0.6
0.8
1
qs,c
qbed
qs,w
(b)
dzi/d
t (m
3 /m2 s)
×10-4
-2
-1
0
1
2
− 11−ε0
dqsdx
− 11−ε0
dqbeddxdzbed
dt
accretion
erosion
(c)
x (m)50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
z (m
)
-1.5
-1
-0.5(d)
0 min.90 min.
Chapter 4
124
Along the lee side of the bar and shoreward from the plunge point (x = 56.0 – 57.0 m), both qsand qbed increase in magnitude. Magnitudes of offshore directed qs exceed those of onshoredirected qbed by about a factor 2 (frel 0.7 for qs; frel 0.3 for qbed). The physical explanations forthe increase in both transport components is notably different: qsusp increases due to thecombination of strong near bed undertow velocities and enhanced sediment pick up bybreaking generated turbulence, while qbed increases primarily due to bed slope effects. Furthershoreward at bar trough and inner surf zone locations (x 58.0 m), both transport componentsdecrease in magnitude and the established relative contributions by qsusp (frel 0.7) and qbed (frel0.3) remain approximately constant.
4.5.2 Bedload and suspended load transport contributions to bed profile change
Figure 4.11c shows the negative cross shore gradients (–d/dx) of qs and qbed, divided by thesediment fraction in a loosely packed bed (1 – 0; with porosity 0 = 0.4). These terms can beinterpreted as the contributions by both transport components to local bed level changes. Thesigns are chosen such that positive values correspond to net local accretion, and negativevalues to net erosion, of the bed.
Figure 4.12. Vector plot of transport rates and transport gradients, time averaged over t=0 90 min, ofdepth integrated suspended load (panel a) and bedload (panel b) transport. Bed parallel arrows
(black) denote cross shore transport rates, consistent with Figure 4.11a. Vertical arrows are cross shoregradients of each transport component, with red (upward) indicating a positive gradient dq/dx(corresponding to local erosion) and blue (downward) corresponding to negative dq/dx (local
accretion). Bed profile (solid black line) is at t=0 min. Transport gradients with magnitudes < 1.0 10 5
m3/m2s were truncated for illustration purposes.
Suspended transport leads to erosion of the bar trough (x = 56.5 – 58.0 m) and accretion of thebar crest and higher ends of the shoreward bar slope (x = 54.0 – 56.5 m). Bedload transportleads to accretion of the breaker bar (x = 52.0 – 55.5 m), erosion of the shoreward bar slope (x =
z (m
)
-2
-1
0
break point plunge point splash point
(a) Suspended load
x (m)50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
z (m
)
-2
-1
0
b.p. p.p. s.p.
q=10-4 m3/ms-dq/dx=2*10-5 m3/m2s
(b) Bedload
Bedload processes and breaker bar morphodynamics
125
55.5 – 56.5 m) and accretion of the breaker trough (x = 56.5 – 58.0 m). Hence, the net bed levelchange between x = 55.0 and 58.0 m (bar crest to bar trough) is explained by the net differencebetween opposite contributions by suspended load and bedload. Suspended load transportcontributions to the bar morphodynamics exceed those by bedload, which explains the growthof the bar crest and deepening of the bar trough during the experiment.
Figure 4.12 shows the suspended load (panel a) and bedload (panel b) transport rates again,but this time as a vector plot along the bar profile and in combination with their effects on localbed level changes. The figure illustrates how sediment advection occurs as suspended and bedload in opposite directions, and how both components lead to local bed erosion or accretion.Suspended transport particularly reveals net sediment pick up in the bar trough. Onceentrained, suspended grains are advected offshore and upwards along the lee side of the barby the undertow. The offshore directed suspended transport increases in offshore directionalong the lee side of the bar, due to enhanced entrainment by breaking generated TKE(Chapter 3). Suspended sediment is deposited at the bar crest where both undertowmagnitudes and TKE levels decrease (compared to shoreward locations).
Bedload transport rates are large at shoaling locations (x = 51.0 and 53.0 m) and reduce towardsthe breaker bar. This leads to net sediment deposition by bedload transport between the breakpoint and the bar crest (x = 53.0 – 54.5 m). Bedload transport rates increase along the lee sideslope of the bar, due to bed slope and possibly because of increased near bed TKE levels. Thislee side bedload transport leads to erosion of the bar crest and accretion of the bar trough(Figure 4.12b) and counterbalances a large part of the bar accretion induced by the suspendedsediment transport (Figure 4.12a).
4.6 Grain size sorting
This section examines the vertical grain size sorting in suspended sediment (Section 4.6.1) andthe cross shore sorting along the bed surface of the breaker bar (Section 4.6.2). The latter isrelated to size selective transport as bedload and suspended load.
4.6.1 Vertical sorting of suspended sediment
Figure 4.13 shows vertical profiles of the median diameter (D50) of suspended sediment,sampled with a six nozzle Transverse Suction System (TSS). Profiles of D10 and D90 arequalitatively similar and are not shown here for brevity. Different behavior is observed forlocations relatively far offshore/shoreward from the plunge point, i.e. at the shoaling locationx = 51.0 m and at inner surf zone locations x = 59.0–63.0 m, versus the locations in the breakingregion (x = 54.5–58.0 m).
At the shoaling and inner surf zone, it is firstly shown that the D50of particles in suspension issubstantially lower than the meanD50 in the flume (grey line). Secondly, vertical sorting occurs,as the suspended sediment becomes finer with distance from the bed. At inner surf zonelocations (x > 58.5 m), the D50at the highest TSS nozzle ( =0.53 m) is systematically larger thantheD50 measured closer to the bed (at =0.31 m). A possible explanation is that the sand fractionat =0.53 m contains a larger fraction of sediment that is entrained in the breaking region andthen advected to the inner surf zone at elevations above wave trough level (see Chapter 3).
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126
D50 (mm)0.20 0.30
ζ (m
)
0
0.1
0.2
0.3
0.4
0.5
0.6
shoaling zonex=51.0 m
0.20 0.30
x=53.0 m
0.20 0.30
breaking zonex=54.5 m
0.20 0.30
x=55.0 m
0.20 0.30
x=55.5 m
0.20 0.30
D50 bed
x=56.0 m
D50 (mm)0.20 0.30
ζ (m
)
0
0.1
0.2
0.3
0.4
0.5
0.6 x=56.5 m
0.20 0.30
x=57.0 m
0.20 0.30
x=58.0 m
0.20 0.30
inner surf zonex=59.0 m
0.20 0.30
x=60.0 m
0.20 0.30
x=63.0 m
Similarly, the suspended sediment at x = 51.0 m is not necessarily entrained locally, but mayinstead consist of the finest fractions of sediment particles that are picked up in the breakingregion and then advected offshore.
In the breaking region (x = 54.5 to 58.0 m), large suspended sediment concentrations werefound up to the water surface due to large pick up rates and strong vertical mixing (Chapter3). Figure 4.13 shows little vertical segregation in D50 for this region, particularly for thelocations +/ 1 m from the plunge point (at x = 55.5 m). The suspended sediment appears to bewell mixed and also the coarsest particles are carried to high elevations (up to water surface).Moreover, theD50 of suspended sediment is almost the same as the meanD50 of the initial bed.
Figure 4.13. Vertical profiles of median diameter (D50) of suspended sediment particles at the 12measurement locations. Markers denote means (squares) and 95% confidence interval (horizontal
error bars) over six runs (t=0 90 min.). Black triangles at =0 denote the measured D50 of the bed at theend of the experiment (t=90 min.). Vertical grey lines denote the mean D50 of the original bed.
The different sorting behavior for shoaling and inner surf zone versus the breaking region canbe related to the processes responsible for sediment pick up and vertical mixing. Davies andThorne (2016) detail how for vortex rippled beds, vertical mixing of particles is due tocombined convection (by relatively large coherent periodic vortices ejected from the bed) anddiffusion (by random turbulent fluctuations). Convection becomes increasingly important interms of sediment entrainment and mixing for the coarser fractions in a sediment mixture(Davies and Thorne, 2016). At the shoaling and inner surf zone, turbulent vortices areprimarily bed generated and have a relatively small time and length scale. These small vorticeslead to size selective pick up and also to vertical segregation of suspended sediment due to
Bedload processes and breaker bar morphodynamics
127
D50
(mm
)
0.2
0.25
0.3
0.35 (a)
Initial profileReference profileFinal profile
x (m)50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
z (m
)
-1.5
-1
-0.5 (b)Initial horizontal profileReference bed profile (t=0 min.)Final bed profile (t=90 min.)
differences in vertical mixing and settling for each sediment size fraction, as shown for sheetflow conditions in an oscillatory flow tunnel (Hassan, 2003) and for rippled beds underuniform non breaking waves (Sistermans, 2002; Davies and Thorne, 2016). In the wavebreaking region, turbulent vortices are of larger scale and are more energetic (van der A et al.,Submitted), i.e. have a strong convective mixing capacity for a broad particle size range.Consequently, vertical suspended sediment particle size sorting is restricted under breakingwaves (see also Wang et al., 1998).
4.6.2 Cross shore sorting in the bed
Figure 4.14a shows the cross shore variation in D50 of bed samples for three stages of bardevelopment. Starting with an almost homogeneous grain size distribution along the testsection, evident size sorting occurs throughout the experiment, resulting in a distinct patternof grain distribution at the end of the experiment.
At the locations along the offshore slope of the bar (x = 51.0 to 54.0 m), the D50 decreases intime. Considering the bedload and suspended load transport patterns (as discussed in theprevious sections), the temporal evolution in D50 can be related to two processes: first, netremoval of the coarsest grains in the mixture through selective sheet flow transport (de Meijeret al., 2002; Hassan and Ribberink, 2005); second, the net deposition of fine suspended particlesthat are advected offshore from the inner surf and breaking zone, particularly by the undertow(c.f. Sistermans, 2002). The second process (offshore transport of fine particles) also explainsthe measured coarsening of the bed at inner surf zone locations (x > 58.5 m). This leads to anoverall trend of increasing D50 from shoaling to inner surf zone that is consistent with fieldobservations (Murray, 1967; Richmond and Sallenger, 1984).
Figure 4.14. (a) D50 of sand bed top layer during three stages of bed profile evolution: start of theexperiment with horizontal test section (dot dashed grey line); after initial 105 min start up stage, i.e.reference bed profile at t=0 min. (solid black line); at the end of the experiment, i.e. final bed profile att=90 min (black dashed line). (b) Bed profiles corresponding to three bed development stages in (a).
Chapter 4
128
The region around the breaker bar does not obey this overall trend; additional sortingmechanisms seem relevant. Slightly offshore from the bar crest (at x = 54.5 m) theD50 increases,which can be related to the transport of relatively coarse particles as sheet flow, which aredeposited at the bar crest (see also Figure 4.12). Slightly shoreward, at the bar crest and thehighest elevations along the bar lee side (x = 55.0 – 56.0 m), the diameter decreases. Netdeposition of suspended grains occurs at these locations (see Figure 4.12). However, at theselocations the grain size of suspended particles is significantly coarser than the particlesforming the bed (Figure 4.13) and consequently, this deposition cannot explain the decreasingD50 in the bed. Instead, it is explained by the gravity driven bedload transport along the steeplee side of the breaker bar (Figure 4.12). Coarser grains in a sediment mixture have a largertendency to be transported downslope than finer grains (lee side sorting). This downslopecoarsening along slopes has been shown by several studies in steady flow conditions (seeKleinhans, 2004, for an overview). The relatively coarse sediment at the breaker trough (x =56.5 – 58.0 m) supports this explanation.
4.7 Discussion
Bedload transport rates qbed are obtained indirectly by subtracting the depth integratedsuspended load qs from the total load qtot that was obtained from the bed profile evolution. Dueto propagation of errors in the data treatment steps, the obtained bedload transport rates aresubject to relatively large uncertainties. A quantitative indication of the random errormagnitude was obtained by calculating the standard deviation over six runs at the same crossshore location (see Figure 4.11a). Unfortunately, these uncertainties in the estimated bedloadtransport rates cannot be easily overcome, because direct measurements of bedload transportrates in such a challenging measurement environment are extremely difficult with existinginstrumentation. Two observations justify the use of the indirectly obtained bedload transportrates: first, the indirect estimates of qbed are consistent with estimates of the wave averagedsheet flow layer transport from CCM+ measurements (Figure 4.9a); second, qbed scales similarlyto hydrodynamic forcing as previous transport observations of medium sand sheet flowtransport by Schretlen (2012) (see Figure 4.10a).
Bedload transport is defined here as the transport that occurs at < 0.005 m above theundisturbed bed level. This choice affects some results, for example the absolute bedloadtransport rate and the ratio between bedload and suspended load transport, and it requiressome reflection. If the reference elevation would be raised to the WBL overshoot elevation (at
0.02 m), the ratio between bedload and suspended load transport would not changedrastically since most (80 to 90%) of the suspended load transport occurs at outer flowelevations above the WBL (Chapter 3). Results will likely be more sensitive to a decrease inreference elevation, due to the strong vertical concentration gradient inside the sheet flowlayer. Nevertheless, previous medium sand sheet flow measurements showed that themajority of sheet flow transport is due to horizontal fluxes in the pick up layer, i.e. at < 0(Schretlen, 2012). Consequently, we do not expect the results to be very sensitive if anotherreference elevation had been chosen (within the range 0 < < 0.02 m).
Total transport in the present study is formed by bedload and suspended load contributionsthat are of similar magnitude but of opposite direction. This is consistent with other transport
Bedload processes and breaker bar morphodynamics
129
estimates around breaker bars in wave flumes (Van der Werf et al., 2015, using data ofRoelvink and Reniers, 1995; Grasmeijer and Van Rijn, 1997). Note that some field studies onfine to medium grained beaches suggested that bedload transport under plunging breakersis minor and total transport is almost completely ascribed to suspended transportcontributions (Thornton et al., 1996; Gallagher et al., 1998; Ruessink et al., 1998; Grasmeijer,2002). However, in these studies the bedload transport rates were not measured, but insteadthey were quantified using empirical sand transport models that may not be fully valid (e.g.acceleration skewness effects are neglected) and may potentially lead to large errors.
Bedload and suspended load transport contribute differently to breaker bar morphodynamics(Figure 4.12). Bedload contributions to bar migration have been explained in terms of crossshore varying acceleration skewness (Elgar et al., 2001). The present study supports this, andsuggests that the bed slope is an additional dominant factor that controls cross shore varyingbedload transport rates and, consequently, breaker bar growth and migration. Suspendedsediment transport leads to net sediment pick up at the bar trough and net deposition at thebar crest. This is explained by cross shore variation in undertow velocities and in sedimentpick up rates, the latter being partly driven by breaking generated TKE (Chapter 3). Note thatDyhr Nielsen and Sorensen (1970) highlighted the spatially varying undertow as a governingfactor for breaker bar morphology. In addition, Zhang and Sunamura (1994), based on smallscale wave flume observations, qualitatively describe the effect of cross shore varyingbreaking generated turbulence on breaker bar bed level changes. The present study supportsthese governing bedload and suspended load transport mechanisms for breaker barmorphodynamics by quantifying, possibly for the first time, the simultaneous contributionsby both transport components to bed level changes along a large scale breaker bar.
The hydrodynamics along the breaker bar are strongly non uniform: parameters that affectsediment transport (e.g. periodic and time averaged velocity, near bed TKE, bed slope) canchange substantially over a small cross shore distance. If this distance is smaller than thedistance covered by advected fluid mass during a wave cycle (i.e. twice the semi excursionlength in a situation without currents), one may expect that net sediment transport is notpurely controlled by local hydrodynamic forcing but also by forcing at adjacent cross shorelocations that affect the intra wave advection of sediment. It follows from Table 4.1 and Figure4.3 that the flow is particularly non uniform at the locations between the bar crest and bartrough. Indeed, sheet flow observations at the bar crest (x = 54.5 m) suggest that the horizontalsediment influx during the wave trough phase may lead to an increased sheet flow layerthickness. Such horizontal sediment advection effects on sheet flow concentrations have alsobeen shown for the swash zone (van der Zanden et al., 2015a), yet they mark a clear differencewith uniform wave conditions where the sheet flow layer dynamics can be purely explainedin terms of local hydrodynamics (e.g. Schretlen, 2012).
A crucial question is whether this influx of horizontally advected sediment has a significanteffect on the local sheet flow sediment transport rate at x = 54.5 m. The sheet flow layerthickness increases by approximately 1.5 mm for a duration of about 1 s during the wavetrough phase. By assuming that horizontal advection primarily affects the upper sheet flowlayer, where typical concentrations are 0.1 m3/m3 and particle velocities are approximately 0.8m/s, the surplus wave averaged sediment transport rate associated with the trough phaseincrease in sheet flow thickness equals approximately –0.1 kg/ms. This is of the same order of
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magnitude as bedload transport rates across the test section (Figure 4.9). Consequently, thearrival of offshore advected sediment during the trough phase may partly explain thesignificantly lower bedload transport rates at x = 54.5 m compared to offshore locations (x =51.0 and 53.0 m).
Interestingly, the estimated bedload transport rates along the shoreward bar slope are directedonshore, while near bed velocities are directed offshore during almost the entire wave cycle.Hence, bed shear by phase averaged velocities cannot be the only mobilizer of bedloadparticles and instead, bed slope and possibly breaking generated TKE have significant effects(Figure 4.10). Physically, the effects of breaking generated turbulence on bedload transportare explained as follows. Small scale wave flume observations revealed that the intermittentarrival of breaking generated turbulence at the bed can result in instantaneous bed shearstresses in both onshore and offshore direction with magnitudes several times the time andphase averaged bed shear stress (Cox and Kobayashi, 2000; Sumer et al., 2013). The occurrenceof such intermittent turbulence events at the bed is random, i.e. it does not correlate with aspecific phase of the wave cycle (Cox and Kobayashi, 2000). The intermittent large bed shearstresses will mobilize particles which on a sloping bed will be transported downslope bygravity. Such a combined effect by TKE and bed slope may be the physical mechanism behindthe observed onshore transport along the lee side of the bar in the present study. Suchtransport could for instance be modeled as a separate component to bedload transport usinga deterministic formulation with bed slope and breaking generated turbulence as main inputparameters (e.g. Fernández Mora et al., 2015). The present data cannot be used tounambiguously assess the individual effects by near bed TKE and local bed slope on bedloadtransport, due to significant covariance between both controlling parameters in the breakingregion. Additional physical or numerical experiments would be required to furtherunderstand the effects of breaking generated turbulence on bedload transport and to accountfor these effects in bedload transport models.
Grain size distributions of suspended particles reveal size selective pick up and verticalsorting at the rippled bed inner surf zone, but approximately size indifferent entrainment andmixing in the breaking region. Numerical simulations have demonstrated that selectivetransport in the surf zone may importantly affect breaker bar morphodynamics (Van Rijn,1998). However, model formulations for size selective pick up at plane beds (e.g. Van Rijn,2007) may need to be adapted in order to simulate the size indifferent pick up under plungingwaves that also brings the coarser sand grains into suspension.
4.8 Conclusions
We present measurements of sand transport processes and transport rates along an evolvingmedium sand breaker bar under a large scale plunging breaking wave. Measurements of thesheet flow layer were obtained at two cross shore locations near the crest of the breaker barusing CCM+. Grain size sorting was studied through samples of suspended sediment and ofthe bed top layer. The total transport rate was split into a depth integrated suspendedtransport rate and a bedload transport rate, which were both assessed to obtain a completeoverview of the governing transport contributions to breaker bar development. From theresults we conclude:
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1. The sheet flow thickness at the offshore bar slope scales similarly to hydrodynamicforcing as previous observations under non breaking waves. At the bar crest,horizontal sediment advection along the bed affects sheet flow concentrations andthicknesses during the wave trough phase due to a positive influx of sediment fromthe plunge point. The time varying transport rate depth integrated over the sheet flowlayer is of similar magnitude as the time varying suspended sediment transport rate.
2. The net (i.e. wave averaged) total transport rate consists of a generally onshoredirected bedload and an offshore directed suspended load component, which are ofsimilar magnitude. Bedload transport dominates at the shoaling zone, decreases at thebar crest, and increases again at the shoreward facing bar slope. The latter is explainedby bed slope effects (i.e. gravity driven transport) and occurs in the presence of highnear bed turbulent kinetic energy, that possibly enhances the mobilization of sandgrains. The suspended load increases in the breaking region, leading to a dominationof suspended transport over bedload transport in the breaking and inner surf zone.Consequently, near the plunge point the net total transport reverses from onshoredirected (shoaling zone) to offshore directed (breaking and inner surf zone).
3. During the experiment, the breaker bar crest increases in height while the bar troughdeepens. Both bedload and suspended sediment transport contribute to breaker barmorphodynamics, but the effect of each component is notably different. Bedloadtransport leads to erosion of the offshore slope and accretion at the bar crest, andadditionally leads to erosion of the steep shoreward bar slope and deposition at the bartrough. Suspended transport induces erosion of the bar trough, offshore and upwardadvection of sediment by the undertow along the shoreward bar slope, and netdeposition at the breaker bar crest.
4. Suspended sediment samples show evidence of vertical grain sorting at the shoalingand inner surf zone, which indicates that sediment pick up and vertical mixing is sizeselective (i.e. the fraction of fine sediment increases with elevation). This contrasts withthe breaking region, where sediment pick up and vertical mixing is size indifferentdue to the large scale energetic vortices (strong upward forcing). Bed samples revealcross shore sorting of sand particles by size selective transport as bedload andsuspended load. This sorting leads to a gradual increase in sediment size from shoalingto inner surf zone and reveals additional local sorting around the breaker bar due tobed slope effects (i.e. downward coarsening along the steep shoreward bar slope).
Measurements from the same experiment were used previously to study the effects of wavebreaking on wave bottom boundary layer hydrodynamics (Chapter 2) and on suspendedsediment processes (Chapter 3). All combined, the studies offer a detailed insight into thecomplex spatiotemporally varying hydrodynamics and sediment dynamics along a breakerbar under a plunging wave.
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5 Laboratory measurements of intraswash bed level and sheet flowbehavior
Highlights: Bed levels respond to individual swash events and to sequences of events. The bed erodes during the uprush and accretes during the backwash phase. Sheet flow characteristics are not fully locally determined.
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Abstract
Detailed measurements of bed level motions and sheet flow processes in the lower swash arepresented. The measurements are obtained during a large scale wave flume experimentfocusing on swash zone sediment transport induced by bichromatic waves. A new instrument(CCM+) provides detailed phase averaged measurements of sheet flow concentrations, particlevelocities, and bed level evolution during a complete swash cycle. The bed at the lower swashlocation shows a clear pattern of rapid erosion during the early uprush and progressiveaccretion during the middle backwash phase. Sheet flow occurs during the early uprush andmid and late backwash phases. Sheet flow sediment fluxes during these instances are highestin the pick up layer. Sediment entrainment from the pick up layer occurs not only duringinstances of high horizontal shear velocities but also in occurrence of wave backwashinteractions. As opposed to oscillatory sheet flow, the pivot point elevation of the sheet flowlayer is time varying during a swash event. Moreover, the upper sheet flow layerconcentrations do not mirror the concentrations in the pick up layer. Both differences suggestthat in the lower swash zone the dynamics of the upper sheet flow layer are not only controlledby vertical sediment exchange (such as in oscillatory sheet flows) but are strongly affected byhorizontal advection processes induced by the non uniformity of the flow.
__________________________________________________________________________________This chapter has been published as:Van der Zanden, J., Alsina, J. M., Cáceres, I., Buijsrogge, R. H. and Ribberink, J. S. (2015). Bedlevel motions and sheet flow processes in the swash zone: Observations with a new conductivity basedconcentration measuring technique (CCM+). Coastal Engineering 105: 47 65. doi:10.1016/j.coastaleng.2015.08.009.
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5.1 Introduction
The swash zone is the area that connects the surf zone to the emerged beach. This zone ischaracterized by the alternating exposed and submerged state of the bed. The swash is a highlydynamic area where water and sediment flows occur within a highly transient, aerated, andshallow water layer. The hydrodynamic forcing occurs at both short and long wavefrequencies and as a result, also bed levels experience rapid and large changes at similarfrequencies as the waves (Puleo et al., 2014). Magnitudes of sediment fluxes in the swash arelarge and various modes of transport (sheet flow, suspended load) may coexist (Masselink andHughes, 1998). Moreover, interactions between incident waves and bores with precedinguprush or backwash result in rapid alteration of the flow field, increased turbulence, andenhanced sediment suspension during a swash event (e.g. Hibberd and Peregrine, 1979;Hughes and Moseley, 2007; Masselink et al., 2009; Blenkinsopp et al., 2011; Caceres and Alsina,2012).
The small water depths and the continuous alternating state of the bed (exposed, submerged)make it extremely challenging to measure and understand the sediment dynamics andhydrodynamics in detail. Our present knowledge of the swash zone sediment dynamics isprimarily based on measurements of near bed sediment concentrations (Aagaard and Hughes,2006; Alsina et al., 2012), estimations of sediment transport from inter wave bed level changes(Turner et al., 2008; Blenkinsopp et al., 2011), or sediment trap measurements (Baldock et al.,2005; Alsina et al., 2009). Common instruments particularly fail at obtaining high qualitymeasurements of (i) sheet flow dynamics and (ii) bed level evolution throughout completeswash events (for both exposed and submerged state).
Sheet flow is a sediment transport mode that occurs during highly energetic flow conditions.When near bed velocities are sufficiently high, sand transport is confined to a highconcentration (100 to 1600 g/L) layer with a typical thickness of 10 to 100 times the graindiameter (Ribberink et al., 2008). The high cross shore sediment fluxes in this layer contributeimportantly to net transport rates in the near shore region (Ribberink and Al Salem, 1995).Sheet flow dynamics have been studied extensively for uniform oscillatory flow conditions inlaboratories, i.e. oscillatory flow tunnels (e.g. Horikawa et al., 1982; O’Donoghue and Wright,2004a; van der A et al., 2010) and wave flumes (e.g. Dohmen Janssen and Hanes, 2005;Schretlen, 2012). The sheet flow layer can be divided into a pick up/deposition layer and anupper sheet flow layer, which are respectively found below and above the still water bed level(Ribberink et al., 2008). During a wave cycle, the vertical concentration gradient changescontinuously as a result of vertical sediment exchange. More specifically, the concentrationprofiles pivot around a vertical reference point (pivot point) which marks the top of the pickup layer and which is at an approximately fixed elevation throughout the wave cycle(O Donoghue and Wright, 2004a).
Sheet flow transport has been highlighted as an important contributor to swash zone sedimenttransport (Yu et al., 1990; Beach et al., 1992; Jackson et al., 2004; Masselink and Puleo, 2006).However, knowledge on swash zone sheet flow dynamics is limited since only fewinstruments are capable of obtaining high quality measurements of sheet flow concentrations.Conductivity based instruments showed the occurrence of sheet flow during early uprush andlate backwash instances (Yu et al., 1990; Lanckriet et al., 2013; Lanckriet and Puleo, 2015).
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Vertical concentration profiles during isolated backwash events, measured with a recentlydeveloped Conductivity Concentration Profiler (CCP), showed strong similarities toobservations for oscillatory sheet flow (Lanckriet et al., 2014). During the early uprush, thesheet flow thickness may be larger than for oscillatory flows with similar hydrodynamics andsediment characteristics (Lanckriet and Puleo, 2015). This increased thickness is likelyattributed to additional bore turbulence (Lanckriet and Puleo, 2015). Despite these recentadvances, the number of studies on sheet flow layer dynamics in the swash is still limited anddoes not cover the full range of swash hydrodynamics. In particular, no studies have been ableto quantify sediment fluxes for swash zone sheet flow.
In terms of bed level measurements, only few instruments are able to sample the bed duringboth submerged and exposed state (see Puleo et al., 2014, for an overview). Theaforementioned CCP seems to be the only instrument with sufficient accuracy (1 mm) andtemporal resolution (sampling > 1 Hz) to study the intra wave bed evolution in detail. Fieldmeasurements of the CCP in the inner surf and lower swash zone show how mean bed levelsdecrease or increase almost monotonically during a swash event (Puleo et al., 2014). It has beenshown that swash events with relatively high onshore velocities and long onshore duration(compared to offshore velocities and duration) are more likely to induce erosion of theseaward swash region, while local accretion is predominantly caused by events with strongeroffshore velocities and longer backwash duration (Puleo et al., 2014). Previous experimentalstudies have not addressed the effects of wave swash interactions on intra event bed levelchanges. In addition, previous studies did not connect the intra event bed level observationsto sheet flow dynamics and sediment fluxes.
The limited knowledge on swash zone sediment transport processes and fluxes hampers thedevelopment of improved swash zone sediment transport formulae that can be applied inmorphologic models. Energetics based sediment transport models, which are commonly usedfor the near shore region, often fail at predicting adequately the sediment transport rates inthe swash zone (Masselink et al., 2009). One of the main reasons is that sediment transportrates in the swash are not fully determined by local hydrodynamics as advection of presuspended sediment is important too (Pritchard and Hogg, 2005; Alsina et al., 2009).
In this paper we present the results of recent large scale wave flume experiments withbichromatic waves focusing on intra event bed level variations and sheet flow dynamics. Thelaboratory setting allows us to generate repeatable swash events and to study sedimenttransport processes in great detail. The main objectives of the paper are (i) to study bed levelevolution and (ii) to characterize the dynamics of the sheet flow layer in the lower swash zone.
High quality measurements of the bed level and sheet flow concentrations and particlevelocities are obtained through a new conductivity based measuring instrument (CCM+)which is presented in Section 5.2 and evaluated in Appendix 5.A. The experimental set up andwave conditions are presented in Section 5.3, followed by the beach profile evolution (Section5.4). Section 5.5 presents bed level measurements at different time scales. Section 5.6 presentsmeasurements of the sheet flow dynamics in the lower swash zone. Finally, we reflect on theobtained new insights and their connection to existing knowledge on swash zone and sheetflow dynamics and to sediment transport modeling (Section 5.7).
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5.2 Description of CCM+
The CCM+ system is based on existing CCM technology (c.f. Ribberink and Al Salem, 1995;McLean et al., 2001; Dohmen Janssen and Hanes, 2005). Previous CCM versions requiredconstant repositioning of the measuring sensors in order to cope with the time varying bedlevel. Moreover, they relied on another instrument for a measurement of the reference bedlevel. In the new CCM+ technology, these problems are overcome with a new tracking systemthat allows automatic repositioning of the sensors. Sheet flow concentrations are measured byone pair of sensors, while an independently operating third sensor is used to measure the bedlevel.
5.2.1 Hardware
The exterior of the CCM+ tank is formed by a closed stainless steel cylinder with a 0.48 mdiameter and height of 0.63 m (Figure 5.1). The tank is welded to a steel base plate that can bemounted to the flume bottom or a palette, which in combination with the heavy weight (70kg) of the tank ensures the stability for compensating buoyancy and other destabilizingmechanisms. The probes containing the measuring sensors are mounted to two slim stainlesssteel rods that emerge from the tank. Both rods operate independently and can move verticallyover a range of 28 cm. Their positions are controlled with sub mm accuracy by electromagneticservomotors within the tank. O rings prevent water and sand intrusion. The tank is equippedwith a total of three probes (Figure 5.2, top left). Probes 1 and 2 are mounted to the same rod,while a third probe is mounted to the second rod. Reference to the former, combined probe ismade as ‘probe 1/2’.
Figure 5.1. SolidWorks image of CCM+ tank with three sensors.
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The sensors in the top of each probe are formed by four platinum electrodes with a thicknessof 0.3 mm and spacing of 0.6 mm, covered by an epoxy topping such that the exposed part ofthe electrodes is 0.8 mm high (Figure 5.2, top right). The two sensors on probe 1/2 are alignedin cross shore flow direction with 1.5 cm spacing, and can be used to determine sedimentvelocities through cross correlation of the high pass measured signal (McLean et al., 2001).Sensors 1/2 and sensor 3 are co located in terms of cross shore position and separated 9 cm inlongitudinal direction.
Figure 5.2. Photos of CCM+ system. Top: probes in lowest position (left) and probe sensors (right).Bottom: installation of tanks during an experiment (left) and zoom of probes after installation (right;
note that during an experiment, the probes are lowered such that only the probe sensors emerge fromthe bed).
The measuring principle of the sensors is conductivity based. An alternating current isgenerated over the outer two electrodes while the inner two electrodes measure the electricalresistance of the water which is translated to a voltage Um. This voltage can be translated to asediment volume concentration C (m3 sand/m3 mixture):
calm
fUU
C )1( 0 (5.1)
whereU0 is the reference voltage for clear water (V) and fcal is a dimensionless calibration factorthat usually approaches unity. Both U0 and fcal depend on probe characteristics and in situ
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water conditions. Before the start of an experiment, the voltages in clear water and in a looselypacked sand bed are measured in order to calibrate the measurements.
During an experiment, the tank and rods are fitted into the sand bed and only the probesensors reach into the sheet flow layer (Figure 5.2, bottom). In the lowest position, the sensorsin the tips of the probes are at 14 cm above the tank. Hence, the tank itself is always far fromthe bed and is not expected to affect sediment transport.
The sampling volume of the probe was assessed by moving the probe up and down a sandbed (grain diameter D50 = 0.24 mm). The calibration graphs showed a concentration changefrom 0.10 to 0.90 times the volumetric concentration in the bed over a vertical range of 1.5 mm.This indicates that the sampling volume of the sensor extends vertically up to 1 2 mm. Duringinitial pilot tests, the sensors were vertically positioned in the upper half of a water columnthat was frequently aerated by wave collapsing. The conductivity measurements did notreveal a noticeable change in signal as a result of bubble presence.
5.2.2 Signal processing and bed level tracking system
Within the CCM+ system, two types of signals are sampled: (i) the conductivity measurementsof the sensors; (ii) their vertical positions (z1,2 and z3). The sampling frequency is a set 1000 Hz,which is required for determining the particle velocities.
Figure 5.3. Flow chart of signals in CCM+ system.
Figure 5.3 shows a simplified flow chart of the various subsystems, their main tasks, and the signals between the subsystems. The system is controlled through LabVIEW. An Ethernet cable connects the PC to a Beckhoff PLC control unit inside the control box. The new feedback loop for automatic concentration or bed level tracking is programmed in this unit. The computation step simplytranslates the difference between the measured voltage Um and a set target voltage Ut, thatrepresents a specific target concentration, to a velocity for vertical probe movement:
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ptm kUUv )( (5.2)
where v is the velocity of probe movement (m/s; defined positively upward);Ut (V) is the targetvoltage that corresponds to a target concentration through Equation 5.1; and the ‘gain factor’kp (m/s/V) is an input factor that controls the sensitivity of the probe’s response. A measuredvoltage (concentration) that exceeds the target value results in a positive vertical velocitythrough Equation 5.2, so the probe will move upward. where voltages (hence concentrations)are lower. The speed of movement is proportional to the offset of the measured voltage withrespect to the target value. A typical target value used when tracking the bed is the voltagecorresponding to half the concentration in the loosely packed bed. This ensures that the probemoves continuously towards the interface between bed and water.
The PLC control unit is equipped with a correction for probe exposure to air when measuringin the swash zone, preventing the probes to move upwards when above water. After thecomputation step, the PLC control unit transfers the velocity to two Copley Controls XenusPlus motor controllers inside the tank, which each contain a motion controller that translatesthe velocity to a desired position.The CCM+ electrodes are connected to a sensor interface, which contains a chip that treats themeasured voltage signal (e.g. demodulating and analogue filtering). The analogue positionand voltage (concentration) signals are translated into digital signals by the motor controller.By digitizing the signal near the source, signal distortions are minimized. The bed leveltracking loop is repeated every 0.02 s and the Um value used in Equation 5.2 represents themoving average with a lag of 20 samples (buffering step to reduce effect of signal variations).The performance of the bed level tracking system greatly depends on the system’s ability torespond rapidly and adequately to a concentration offset. Therefore, the signal processingscheme is developed such that a stable vertical probe motion is realized with minimum delaybetween input (measured concentration) and response (probe movement) of the trackingsystem. The probes are able to move with velocities over 0.1 m/s, but the users risk unstableprobe behavior and overshooting of the target concentration level when the applied gain factorvalue is too high.Section 5.3.3 provides more details about the applied tracking system settings of the 3 CCM+
probes throughout the experiment.
5.3 Description of the experiments
5.3.1 Experimental set up
The CCM+ system was applied during the ‘CoSSedM’ experimental campaign that was donein the Canal de Investigacion y Experimentacion Maritima (CIEM) at the UniversitatPolitècnica de Catalunya (UPC), Barcelona. This is a large scale wave flume of 100 m length, 3m width and 4.5 m depth. The aim of the experimental campaign was to study cross shoremorphology and swash zone sediment transport processes under various bichromatic waveconditions of equal wave energy but different modulation periods. In this paper we considerthe measurements for one erosive condition, labeled ‘BE1_2’. For this condition, theexperiment consisted of 8 runs of approximately 30 min.
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The beach consisted of commercial well sorted medium sand with a characteristic diameter(D50) of 0.25 mm, a narrow grain size distribution (D10 = 0.15 mm and D90 = 0.37 mm), ameasured settling velocity of 0.034 m/s, and a porosity of 0.36 when loosely packed. The beachwas shaped to a 1:15 constant slope prior to the experiment (Figure 5.4).The vertical coordinate z is defined positively upwards from the still water level (SWL). Theshoreline (intersect between SWL and initial profile) at the start of the experiment is used ashorizontal datum. Cross shore coordinates x are defined positive towards the beach (onshore)and negative (offshore) towards the wave paddle (Figure 5.4). The toe of the bed profile islocated at x = 42.5 m. waves are generated by the wave paddle at a water depth of 2.48 m andan x position of 75.2 m. Between the wave paddle and the toe of the profile, the waves travelover the concrete bottom of the wave flume.Figure 5.4 includes the instrumentation applied during the campaign. Outside and at the surfzone, water surface elevations were measured through a sequence of Resistive Wave Gauges(RWGs). Most instrumentation was located at the targeted research area (around shoreline),corresponding to the inner surf and swash zones. Here, instruments at various cross shorepositions measured velocities (Acoustic Doppler Velocimeters, ADVs), suspended sedimentconcentrations (Optical Backscatter Sensors, OBSs) and water surface elevation (AcousticWave Gauges, AWGs; Pore Pressure Transducers, PPTs). Two CCM+ tanks were installed closeto the shoreline (Figure 5.4). This paper focuses on the lower swash zone, so results of CCM+
tank 2 are not considered.
Figure 5.4. Wave flume configuration with measured bathymetry averaged over all initial profilesobtained during the experimental campaign. Upper panel: general view with Resistive Wave Gauge
(RWG) positions (vertical black lines); Lower panel: amplification of the beach face area withinstrument locations. Solid squares are Pore Pressure Transducers (PPTs), open squares are Acoustic
Wave Gauges (AWGs), open circles correspond to Optical Backscatter Sensors (OBSs) and starssymbols refer to Acoustic Doppler Velocimeters (ADVs).
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CCM+ tank 1 was located at an x position of 0.60 m shoreward of the SWL intersect. As isshown and discussed later (Section 5.4), this position is within the lower swash zone (followingthe submergence criterion of Aagaard and Hughes, 2006). An AWG and ADV were installedat the same cross shore position. Above the tank, the downward looking AWG measuredwater surface and exposed bed levels with a practical accuracy of about 1 mm and samplingfrequency fs of 40 Hz. The ADV, a Nortek side looking laboratory Vectrino, measured all threevelocity components (fs = 100 Hz). Prior to each experimental run, the ADV was vertically repositioned in order to maintain a constant elevation of 0.03 m with respect to the bed.A mechanical bed profiler, consisting of a pivoting arm and a wheel that are deployed from amobile trolley, was used to measure the beach profile along the centerline of the wave flume.The profiler is able to measure both the sub aerial and the sub aqueous beach and is describedin detail by Baldock et al. (2011). Given the wheel diameter of 0.2 m, the profiler is unable tofollow individual ripples and it has an estimated accuracy of +/ 10 mm (Baldock et al., 2011).Profile measurements were obtained prior to the experiment and after each 30 minute run.
5.3.2 Wave conditions
Throughout the CoSSedM experimental campaign, various types of bichromatic waveconditions were run. Wave condition BE1_2, considered in this paper, is an erosive conditionwhich was expected to lead to highly energetic flow conditions in the swash. The bichromaticwave consists of a frequency component f1 of 0.303 Hz with wave height H1 of 0.30 m and afrequency component f2 of 0.237 Hz with wave height H2 = 0.25 m (Table 5.1). Together theyform a bichromatic wave group with a frequency fgr = f1 – f2 = 0.067 Hz (Tgr = 15.0 s).
Table 5.1. Overview of wave components bichromatic wave condition BE1_2.
Wave component Subscript f (Hz) T (s) H (m)Short wave 1 1 0.303 3.3 0.30Short wave 2 2 0.237 4.2 0.25Wave group gr 0.067 15.0
Repeat frequency R 0.005 195
For this particular condition it is important to note that not all wave groups repeat exactly atthe group frequency. Instead, there is a gradual transition of the short wave phase within thegroup. This type of modulation at the so called ‘repeat frequency’ (fR) has been reported earlierby Baldock et al. (2000). It is emphasized that the modulations at the repeat frequency changethe short wave phase and overall shape of the wave groups, but they have minor effect on thewave energy of the individual groups.For this experiment, fR equals 0.0051 Hz (repeat period TR = 195 s). As a result of themodulations at fR, the short wave phase within the group repeats exactly after 13 wave groupsbut it repeats approximately every second wave group. As will be shown later, the groups thatare similar in terms of short wave phasing are also comparable in terms of hydrodynamicsand sediment dynamics at the CCM+ measuring location (bed level changes; Sections 5.5.2 and5.5.3). This allows us to phase average sheet flow measurements for two different‘characteristic swash events’ that are induced by comparable wave groups.
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Figure 5.5. Time series for a 60 s time slot (four swash cycles) and power spectral densities of waterlevels for one of the semi equilibrium runs, at three x locations: (a,b) resistive wave gauge at x = 67.6m (close to wave paddle); (c,d) resistive wave gauge at x = 9.7 m (around breaker bar); (e,f) acoustic
wave gauge at x = 0.60 m (lower swash zone). Arrows in panel (e) mark the incident surf bores.
Some characteristics of the measured water levels are presented in Figure 5.5 at three crossshore positions. Close to the wave paddle, the spectrum (Figure 5.5b) clearly shows the twowave components (f1 and f2) forming the bichromatic wave group, plus a sub harmonic at thegroup frequency related to the wave group envelope. While the waves propagate towards theshoreline, the energy of the higher frequencies dissipates and is transferred to other harmonicsand to the wave group frequency (Figure 5.5d). This process is well described in literature(Longuet Higgins and Stewart, 1964; Baldock et al., 2000; Janssen et al., 2003). As a result, theshape of the wave group changes. At the CCM+ location in the lower swash, the energy contentis predominant at the wave group frequency fgr (Figure 5.5f).Each swash event at the CCM+ location is characterized by three major surf bores followed bythe backwash (Figure 5.5e). Note that during the final backwash phases, just before the arrivalof the first bore of an event, a thin swash lens of O(mm) may still exist.The results in Figure 5.5 also illustrate how modulations at the repeat frequency fR affect theshort wave phase but not the wave energy of the 15 second groups. The time series revealdifferent shapes of the four swash events, as a result of the short wave phase modulations at
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fR (Figure 5.5e). Evidently, the relative timing of the arrival of the bores differs for each event.The relative phase of the bores within the swash event is found to repeat approximately everysecond event. At the same time, the spectral energy at fR is negligible (Figure 5.5b,d,f). Inaddition, low pass filtering of the AWG measurements showed that water level fluctuationsat the repeat frequency fR were ofO(mm) in the inner surf and swash zone (results not shown).These observations on the effects of the fR modulations are in line with the work of Baldock etal. (2000).
5.3.3 CCM+ settings
Each of the two probes of the CCM+ tank serves a different purpose. Hence, different controlsettings of the bed level tracking system are applied for each probe. As detailed below, probe1/2 is used to measure instantaneous concentration at fixed vertical levels (C(z,t)), while probe3 measures the continuous instantaneous bed level (zbed(t)).Probe 1/2 (sensors 1 and 2) is set to a slow tracking mode (kp= 0.5 m/s/V), which means that interms of vertical repositioning, the probe responds only to gradual bed motions. On an intragroup time scale, the probe can be considered to be on a fixed vertical position. Note that atthis fixed level, sediment concentrations are time varying due to vertical and horizontaladvection processes that occur on time scales shorter than the wave group period. Theconcentration changes at this level are captured by the sensors. In order to capture thecomplete profile of time varying concentrations in the sheet flow layer, concentrationmeasurements are required at different (fixed) vertical levels. This is achieved by varying thetarget concentration (target C values between 0.15 and 0.45 m3/m3). Consequently, probe 1/2slowly traverses through the sheet flow layer providing (intra wave group) concentrationinformation at varying vertical levels under the repeating swash events.Probe 3 is set to a quick tracking mode (kp = 5 m/s/V). The target voltage of the probecorresponds to a concentration of 0.30 m3/m3, which roughly equals half the sedimentconcentration in the bed and which is close to the middle (or ‘pivot point’) of the sheet flowlayer (see O Donoghue and Wright, 2004a). In this way probe 3 is able to follow the evolutionof the interface between sediment bed and water on a wave group averaged time scale (timescales 15 s). This result is used as reference bed level zref for the concentrations measured withprobe 1/2. It should be noted that the control system is not fast enough to allow perfect trackingof the bed at time scales of seconds and shorter. Instead, probe 3 shows a reduced amplitudeand phase delays of about 2 s with the actual intra wave bed level (see Appendix A). In theCCM+ tank set up this high frequency bed level information can still be obtained from theconcentration behavior as measured with probe 1/2 (see Section 5.5.3.3).The results of the CCM+ bed level and concentration measurements are discussed further inthe framework of the swash measurements (see Sections 5.5 and 5.6). Reference is made toAppendix A for more details about the CCM+ performance in terms of bed levelmeasurements.
5.4 Morphological evolution of the swash zone
Figure 5.6a shows the bottom profile evolution during the complete experiment (240 minutes),measured by the wheeled bottom profiler. The mean net transport rates for each run (Figure
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5.6b) were obtained through solving the mass balance by means of integrating the volumechange, starting from the toe of the profile where net transport was known to be 0 (see e.g.Baldock et al., 2011). Figure 5.6 shows a rapid erosion at the shoreline during the first two runs(0 to 60 min.), leading to a semi equilibrium state that is reached after the second run. Duringthe next six runs, net transport at the shoreline is still offshore although the magnitude is minorcompared to the first two runs.
Figure 5.6. (a) Beach profile evolution; (b) net sediment transport rates (Qx) for each profilemeasurement.
A bar forms initially at around x = 9.7 m, migrates slightly offshore, and stabilizes around x =10.0 m. Over the eight runs, the shoreline retreats with 1.95 m. The erosion of the shoreline
includes erosion of the inner surf and mid low swash area (where the CCM+ tank is located),from x = 3.6 m to x = 4.6 m approximately. Furthermore, berm formation and accretion of theupper/mid swash can be observed from x = 4 m to x = 9 m.The shoreline retreat induces a shift in minimum run down location. The swash zone lengthwas visually measured and inspected by linear interpolation of the AWG and PPT signals, andwas found to cover a wave flume extension of 10.4 m (from x = 1.4 to +9.0 m) during the initialrun and of around 9.0 m (x = 0.25 to 9.3 m) during the final run. Positions in the swash zone
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can be characterized depending on the relative exposure duration of the bed. Following thedefinitions of Aagaard and Hughes (2006), the lower swash zone runs from x = 0.25 to 1.6 m(up to 25% of time exposed), the mid swash from x = 1.6 to 4.7 m (25 to 60% exposed) and theupper swash for x > 4.7 m (over 60% exposure time). Hence, the CCM+ tank was situated in thelower swash zone, 0.35 m shoreward from the inner surf zone. This location also correspondsto the outer swash zone following the definition of Hughes and Moseley (2007), being the subregion where wave swash interactions occur – as opposed to the inner swash zone where theswash events are free of interactions.
Figure 5.7. Time series of acoustic wave gauge (grey lines) and bed level measurements by CCM+
probe 3 (black lines), for three time frames: (a) continuous time series for complete experiment (8 runsof 30 minutes); (b) close up of one of the semi equilibrium runs; (c) close up of bed level and
concentration measurements. Open circles in panel (b) mark identified instances of bed exposure;filled circles in panel (c) mark position of sensor 1/2, with colors referring to the instantaneous
concentration measurement. The target concentration of sensor 1/2 for the period in panel (c) equaled0.45 m3/m3.
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5.5 Bed level motions in the lower swash
5.5.1 Spectral analysis
In this section the CCM+ bed level measurements (probe 3) are analyzed in both time andfrequency domain, in order to identify and characterize dominant time scales of bed levelchanges.
Figure 5.8. Mean spectral density function of the bed level measurements (CCM+ probe 3). Averagespectrum of 6 semi equilibrium runs (thick solid line) and 95% confidence interval based on a chi
square distribution with 12 (twice number of runs used) degrees of freedom (dashed lines).
Figure 5.7 presents time series of the CCM+ probe 3 position, for three selected time frameswith increasing level of detail. AWG data is included as a reference. Figure 5.7a shows thegradual erosion during the complete experiment (8 runs of 30 min = 14,400 s). During instancesof bed exposure, the CCM+ levels match well (order: millimeters) with the lower boundary ofthe AWG levels (Figure 5.7a,b). The measured local erosion of the bed over the experiment(magnitude of 0.1 m), agrees with erosion observed in the beach profile measurements (Figure5.6a). While the AWG data can be used to study gradual bed level changes, the CCM+ providesadditional information about the existence of regular bed oscillations at smaller time scales.The bed clearly responds to the passing of the 15 second wave groups (Figure 5.7c).
Figure 5.7c also shows the vertical motion of the ‘slow’ concentration measuring probe CCM+
probe 1/2 (colored circles), lagging behind the actual bed level as measured by the ‘quick’ bedlevel probe 3. Probe 1/2 traverses the near bed layer while measuring concentrations at varyingelevations (see colors). When probe 1/2 is positioned below the bed interface, clearly higherconcentrations are found than when it is positioned above the bed interface. Offsets between
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concentration measurements of probe 1/2 and the depicted bed level by probe 3 are the resultof small local wave flume asymmetries.
The spectrum of the CCM+ bed level measurements is shown in Figure 5.8. To derive thisfigure, power spectral densities (PSDs) were calculated for the measured bed levels by CCM+
probe 3 (after subtracting the gradual erosion trend) with a Fast Fourier Transform. This wasdone for each of the last six runs, when the bed reached a semi equilibrium state (experimentaltime t > 60 min), and the obtained PSDs were subsequently averaged. As discussed earlier (seealso Appendix A) it is expected that bed level spectral energy at frequencies equal to or largerthan the wave group frequency fgr is underestimated.
The spectrum contains dominant peaks at three frequencies, all of which can be related to thehydrodynamics. The highest peak is at a frequency of 0.067 Hz, which corresponds to thefrequency of the bichromatic wave groups fgr (Tgr = 15 s). At this cross shore location, also thewater surface level spectra were shown to be dominated by this group frequency (Figure 5.5f).The other two bed level spectral peaks are not visible in the water surface level spectrum, butcan both be related to the modulation of the short wave phase at the repeat frequency asdiscussed in Section 5.3.2. The peak at 0.005 Hz corresponds to the repeat frequency fR of thewave groups (TR = 195 s), i.e. the frequency at which the sequence of 13 wave groups repeatsexactly. The peaks at 0.031 Hz and a smaller peak at a slightly higher frequency are close tohalf the frequency of the wave group (0.5 fgr =0.033 Hz) and can be related to the short wavephase repeating approximately every second wave group. Apparently, there is a clearresponse of the bed level to the systematically varying short wave phase within the groups –even though the water level spectra show negligible energy at these frequencies. These bedlevel oscillations with a period of TR = 195 s can also be identified from the time series of theexperiment (Figure 5.7a) and are studied in the next section (5.5.2).
5.5.2 Bed level motions at time scale of the wave group sequence (TR = 195 s)
In order to study the bed level motions in more detail, the measurements are phase averagedat different time scales. Due to the observed variability between successive swash events,phase averaging of the CCM+ probe 3 bed level measurements is firstly done for the occurringsequences of 13 swash events (i.e. over the repeat period TR = 195 s). For this analysis, the firstsequence of 13 wave groups and the last incomplete sequence of groups within each run werenot considered. This leaves seven sequences per run, adding up to 42 repetitions of thesequence during semi equilibrium conditions. The ensembles are normalized using the startof the uprush of the first wave group in the time series.
Phase averaged results of the hydrodynamic measurements (water levels and cross shorenear bed velocities u) at the CCM+ cross shore position are found in Figure 5.9. Due toemergence of the ADV probe, the velocity measurements are discontinuous. The relativelysmall standard deviations (Figure 5.9a,b) indicate that the sequences of 13 wave groups repeatthemselves rather well. The individual wave group induced swash events within theensemble (marked by the alternating grey/white backgrounds in Figure 5.9) are also to a largeextent comparable. Each event consists of two or three major broken waves that can beidentified from the water surface levels. Cross shore velocities reveal a strong onshore
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maximum at the start of each uprush with magnitudes up to about 1 m/s. Maximum velocitymagnitudes are measured in the backwash, where offshore velocities reach 1.5 m/s.
Figure 5.9. Phase averaged hydrodynamics and bed level measurements at the CCM+ location for therepeat period TR = 195 s: (a) water level (w.r.t. SWL) measured by AWG, ensemble mean +/ standard
deviation; (b) cross shore velocities measured by ADV, ensemble mean +/ standard deviation; (c)high pass filtered bed level measurements (cutoff frequency 0.004 Hz) by CCM+ probe 3, ensemble
mean and 95% confidence interval; (d) bed level measurements, band pass filtered (high pass cutofffrequency 0.004 Hz and low pass cutoff 0.020 Hz). Grey white background pattern highlights the
various 15.0 s wave groups within the ensemble. Symbols in panel (a) mark the selected events for indepth analysis: swash event of type “A” (blue diamond) and type “B” (red star).
Despite hydrodynamic patterns being largely similar for all groups, subtle differences exist intiming and magnitude of the individual waves composing the swash events. As shown before(Figure 5.5e), the wave groups show better repeatability with every second preceding groupthan with each directly preceding group. This leads to slightly different velocities and wave
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swash interactions for each swash event. These interactions are for some events described inmore detail in the next section.
The bed level measurements required additional processing data processing prior to phaseaveraging. The gradual erosion trend was removed by applying a high pass Fourier filter, witha chosen cutoff frequency (0.004 Hz) that was slightly lower than the frequency of interest(being fR= 1/TR= 0.0051 Hz). In addition, in order to characterize the pattern and magnitude ofthe bed level fluctuations that are exclusively the result of the short wave modulations at fR, aband pass filter was applied (with lower and upper cutoff frequencies of 0.004 Hz and 0.020Hz, respectively). The applied upper cutoff frequency is slightly lower than the lowest spectralpeak associated with the individual wave groups (0.031 Hz, see Figure 5.8). The band passfilter removes both gradual erosion and the bed level oscillations induced by the individualwave group induced swash events. The accordingly obtained phase averaged bed levels areshown in Figure 5.9c,d.
The bed measurements show that for each 15 s event the uprush induces local erosion, that forsome waves continues during the first part of the backwash and which alters to sedimentationduring the later backwash stage (Figure 5.9c). It also becomes evident that, although thegroup to group differences seem small in terms of hydrodynamics, the magnitudes of intragroup bed level oscillations vary substantially (see Section 5.5.3.2 for further discussion). Anadditional larger scale sedimentation/erosion pattern can also be seen: during the first 6groups the bed slowly accretes, while during the following 7 groups a slow erosion processoccurs (Figure 5.9cd). Apparently, the sequence of net erosion/accretion events of each swashevent drives an overall bed level fluctuation at the repeat frequency. The oscillationapproaches a sine form with a period equal to the repeat period (TR = 195 s) and with anamplitude of about 1.5 mm, and it explains the bed level spectrum peak at fR (Figure 5.8).
5.5.3 Bed level motions during individual swash events
5.5.3.1 Selection of characteristic swash eventsA more detailed analysis of sediment transport process measurements by the CCM+ at thewave group time scale requires a substantial amount of repeating wave cycles. This holds inparticular for sheet flow concentration profiles and particle velocities. Phase averaged resultsfor the 42 repetitions of the 195 s sequence (Section 5.5.2) proved to contain too much scatterto draw solid conclusions. Therefore, for this section and Section 5.6, measurements are phaseaveraged at the group period Tgr (= 15 s). Since hydrodynamics and sediment transportprocesses are not exactly the same for each swash event, two selections are made ofcharacteristic swash events within the sequence of 13 groups.
For each selection, wave group induced swash events that induce similar behavior in terms ofhorizontal velocities and bed level changes are chosen. In order to arrive at two ensembles thatare to a large extent complementary, succeeding events were selected. In the following werefer to events of type “A” (marked by blue diamond symbol in Figure 5.9a) and type “B” (redstar symbol). The obtained ensembles (Figure 5.10) consist of 210 repetitions for event A and168 repetitions for event B. For each ensemble, t/Tgr = 0 refers to the arrival of the first bore ofthe swash event.
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Figure 5.10. Phase averaged intra wave bed level measurements of CCM+ system for characteristicswash events “A” (left) and “B” (right). (a,b) water level measurements by AWG; (c,d) horizontal
velocity measurements by ADV; (e,f) high pass filtered (cutoff frequency 0.02 Hz) bed levelmeasurements CCM+ probe 3. All panels contain ensembles (solid grey lines) and ensemble means(dashed black lines). Also depicted in panels e,f is the elevation of the pivot point (solid white line),derived from the concentration measurements of probe 1/2. Arrows in panels a,b mark the arrival of
surf bores that form the swash event.
The selection of the events forming the two ensembles may appear somewhat arbitrary, sincethe selected wave groups do not repeat exactly within the sequence. Consequently, differencesbetween the individual swash events within each ensemble can be observed, for instance interms of timing of the incoming bore during the backwash of event A (t/Tgr = 0.5 to 0.7, Figure5.10a – grey lines). However, the bed level ensemble does not show any enhanced variation atthis instance (Figure 5.10e). Overall there is good qualitative and quantitative agreementbetween the various swash events that form the ensemble. In terms of water levels, it is pointedout that the differences within the two ensembles A and B are small compared to thedifferences between the two ensembles. The latter statement cannot be repeated for thevelocity measurements, which show substantial variation caused partly by turbulent velocityfluctuations that were not removed (Figure 5.10c,d).
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5.5.3.2 HydrodynamicsBoth events are formed by three major incident waves, and are similar in terms of maximumonshore and offshore velocities (Figure 5.10a d). Also the relative duration of uprush andbackwash is similar for both types of swash events. Differences between the events are foundmainly in terms of timing of incident bore arrival. These bores induce differences in terms oftiming and magnitude of wave swash interactions, which are described in the following. Thecharacterization of interactions is supported by visual (video) observations and additionalAWG measurements. Reference is made to existing literature that describes these interactionsin more detail (e.g. Hughes and Moseley, 2007; Caceres and Alsina, 2012).
For swash event A, the early uprush is generated by a single bore. A second bore arrives duringthe uprush, lagging the first bore with about 2 s (wave capture; Peregrine, 1974; Hughes andMoseley, 2007). The backwash formed by these waves reaches offshore directed velocities ofhigh magnitude (up to 1.5 m/s), but gets interrupted by the arrival of a third bore (around t/Tgr= 0.62). The incident bore is halted by the preceding backwash, and the momentum exchangeresults in a stationary bore at/close to the CCM+ location. This stationary bore is the result ofstrong wave backwash interactions and has been compared to a hydraulic jump (Hughes andMoseley, 2007). The injection of air bubbles into the water column and the entrainment ofsediment by this bore (Caceres and Alsina, 2012) may explain the loss of ADV signal despitewater depths being sufficiently large. During the final stage of the swash event (t/Tgr = 0.7 to1), the remainder of the bore is washed seawards by the backwash.
Swash events of type B (Figure 5.10b,d) are characterized by a strong single uprush that resultsfrom the combination of two incident bores (t/Tgr = 0.1 to 0.2). The second bore captures thefront of the uprush, that was generated by the first bore, close to the CCM+ location (waveuprush interactions; Hughes and Moseley, 2007). A third bore arrives at the start of thebackwash (around t/Tgr = 0.32), i.e. at an earlier stage within the swash event cycle than forevent A. In contrast to event A, the incident bore in event B is not completely halted at theCCM+ location but continues to propagate shoreward (weak wave backwash interactions atthe CCM+ location). Subsequently, it results in a stationary bore (strong wave backwashinteractions) about a meter shoreward from the CCM+ location. This bore dissipates and iswashed seaward during the final backwash stage.
Evidently, near bed velocities are not in phase with water levels. Of particular notice are thebackwash velocities for event B, which remain negative while the incident bore passes themeasuring location (t/Tgr = 0.32 to 0.50). The observed (video/AWG measurements) onshorepropagation of the bore suggests that velocities in the top of the water column are directedonshore, while measured near bed velocities are offshore directed. This suggests a strongvelocity shear in the water column, which has been shown to occur for incident bores before(Butt et al., 2004; Cowen et al., 2003).
5.5.3.3 Bed level motionsBed level motions throughout the swash event are quantified in two ways. Firstly, the directintra wave measurements of CCM+ probe 3 are analyzed. Secondly, the bed can be estimatedfrom the time variant vertical concentration profile as measured by probe 1/2. For bothapproaches, intra wave bed level fluctuations are presented with respect to a reference waveaveraged bed level (zref). This wave averaged bed level should include the mean bed evolution
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trend plus the fluctuations occurring at the repeat frequency as displayed in Figure 5.9d.Therefore, zref is given by the low pass filtered (0.020 Hz cutoff) bed level measurement by the‘quick’ CCM+ sensor 3 (z3). The direct intra wave bed level measurements by probe 3 (z’3) areobtained by subtracting zref from z3.
Before extracting the bed from the concentration profiles (probe 1/2), we need to define whichconcentration value adequately represents the bed level. We try to differentiate between localintra group erosion/accretion of the bed as a result of incoming/outgoing sediment advection(this section), and time varying bed level fluctuations as a result of sheet flow dynamics(Section 5.6). Note that for uniform sheet flow conditions, the maximum level of the immobilebed varies in time due to vertical sediment exchange (pick up and deposition). As a result, thislevel seems inappropriate to study net horizontal advection. Instead, we suggest that for asituation with simultaneous sheet flow occurrence and net bed level changes, the intra groupbed level is best represented by the sheet flow pivot point elevation. At the pivot pointelevation, which marks the middle of the sheet flow layer, concentrations in uniformconditions are nearly constant throughout a wave cycle (O’Donoghue and Wright, 2004a).Consequently, changes in the elevation of the pivot point for non uniform conditions are likelydriven by horizontal advection processes and not by vertical exchange of sediment in the sheetflow layer. Section 5.6.1 explains how the pivot elevation was extracted from themesaurements.
For both swash event types, all bed level measurements within the z’3 ensemble show aconsistent pattern of local bed erosion during the uprush and accretion during the backwash(Figure 5.10e f). This confirms previous observations (Figure 5.9). However, as statedrepeatedly, the CCM+ sensors are unable to perfectly track the bed on time scales smaller thanthe swash event (see Appendix A). The pivot point elevation (white lines in Figure 5.10e,f)provides therefore a more accurate estimate of the bed. Evidently, the bed measurements byprobe 3 show a reduced amplitude and a phase lag compared to the pivot elevation.
The time varying pivot point elevation shows a similar pattern as z’3. Rapid local erosionoccurs during the early uprush (t/Tgr = 0 to 0.1) and starts upon arrival of the first incident bore.During the mid backwash phase (t/Tgr = 0.6 to 0.8), the bed accretes to a level close to the stateat the start of the event. This accretion is more gradual than the erosion during the uprush.Although patterns are similar, the magnitudes of the bed level fluctuations differ substantiallybetween the two groups: about 6 mm for swash event A and about 13 mm for swash event B.
The net bed level change induced by a single swash event results from the sum of erosionduring the uprush and accretion during the backwash. The net effect is small compared to thebed level fluctuations during the event. Also in terms of net bed level change, both events aredifferent. Swash event A leads to net accretion (about 2 mm), while event B induces net erosion(about 3 mm) at the lower swash zone. Recall that bed level changes that occur at the repeatfrequency fR were removed before this analysis.
5.6 Sheet flow dynamics
The measured sediment concentrations and grain velocities, as obtained from the CCM+
sensors 1 and 2, are studied at the time scale of the individual wave groups. Existing
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knowledge about oscillatory sheet flow dynamics (Ribberink and Al Salem, 1995;O’Donoghue and Wright, 2004a) is used as a comparison to obtain insights in sheet flowcharacteristics in the swash. The concentrations shown in this section were measured withsensor 2, which proved to be slightly more stable in terms of calibration values than sensor 1.Overall, phase averaged results by sensors 1 and 2 were highly comparable. Hence,perturbations caused by one sensor being in the lee of the other seem to be negligible.
5.6.1 Vertical concentration profiles
Each of the instantaneous concentration measurements C by sensors 1 and 2 was taken at acertain known absolute elevation of the probe (z1/2). To proceed, these concentrationmeasurements are related to the wave group averaged bed through z’1/2 = z1/2 – zref. As the bedis dynamic, the height z’1/2 of a concentration point measurement at a relative instance t/Tgr isdifferent for each swash cycle (see also Figure 5.7c). Through phase averaging, the C(z’,t)values that were obtained at different elevations z’ but at the same relative phase t/Tgr ofrepeating swash events can be combined into time varying vertical concentration profileensembles for each phase. These concentration profiles consist of 210 C(z’,t) points for event Aand 168 for event B (amounts equal total number of repetitive swash events). Next, theseprofiles are for each phase smoothened by taking the median C measurement for vertical binclasses with 0.5 mm step size.
Figure 5.11 shows these vertical concentration profiles for 10 phases of event A. The errorsbars are occasionally high when the number of concentration measurements within anelevation class is small. Even after averaging, some scatter can still be seen. Nevertheless, theprofiles consistently follow concave shapes with concentrations decreasing with height, muchalike observations for oscillatory sheet flow (e.g. O’Donoghue and Wright, 2004a).
As a result of the chosen control settings of the CCM+, the sheet flow layer was not capturedcompletely at all wave phases (Figure 5.11). Therefore, in order to make a quantitativecomparison between sheet flow observations in this experiment and previous observations foroscillatory flow conditions, the empirical model of O’Donoghue and Wright (2004a, from hereon: ODW04) for sheet flow layer concentrations profiles was fitted through the C(z’,t)measurements. Although this model was originally derived for uniform conditions, Lanckrietet al. (2014) and Lanckriet and Puleo (2015) illustrated the applicability of the equation to sheetflow concentration profiles during uprush and backwash in the swash zone. The approach isalso supported by the apparent similarity between the measured concentration profiles inFigure 5.11 and the profiles of O’Donoghue and Wright (2004a). The adopted ODW04 functionreads:
]'[)()(),'(
eb zzt
tCtzC (5.3)
Where C(z’,t) is the volumetric concentration at height z’ (mm) relative to the original bed atinstance t; Cb is the concentration in the bed (=0.64 m3/m3 in this experiment); (t) and areshape factors; and ze(t) is the so called erosion depth of the sheet flow layer at time t whichmarks the bottom of the sheet flow layer.We used a least square method to fit Equation 5.3 through the data. A fixed value of 1.5 wasused for (O’Donoghue & Wright, 2004), while leaving the variables and ze as two free fitting
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parameters. Values for the shape factor are directly connected to the sheet flow thickness(Section 5.6.4). The agreement between fit and measurements is reasonably good, with anaverage coefficient of determination r2 = 0.85.The curve fitting results include quantitative estimates of the time dependent bed/waterinterface or pivot point level (where C = 0.3) and the time dependent lower boundary of thesheet flow layer (C = Cb= 0.64). These elevations were used in Section 5.5.3.3 to study the intrawave bed level behavior (Figure 5.10e,f).
Figure 5.11. Vertical concentration profiles for various t/Tgr instances of wave group A. Panels includemean C(z’,t) values (black dots), standard deviations of mean (vertical error bands), fitted ODW04
curve (thick grey line), and position of the pivot point (triangle + dotted red line).
The time varying nature of sheet flow concentration profiles becomes evident from Figure5.11. For t/Tgr = 0.2 and 0.3, the profiles show a sharp interface between the immobile bed andthe water. This suggests that the bed is at rest (no sheet flow). Note that these instancescorrespond to low near bed velocity magnitudes (c.f. Figure 5.10c). Towards t/Tgr = 0.6 and 0.7,the concentration gradient becomes less steep as the sheet flow layer develops. From t/Tgr = 0.1to 0.7, the pivot elevation is at a more or less fixed level and the temporal variation in vertical
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concentration gradients is attributed to vertical exchange of sediment. At t/Tgr = 0.8, the bedstarts to rise which agrees with bed level measurements of probe 3 (Figure 5.10e).
5.6.2 Time series of sheet flow concentrations
Concentration time series are noisy, and more insights are obtained when focusing at phaseaveraged concentrations obtained at different vertical elevations. Phase averaging is done forsix concentration bin classes, ranging from C = 0 to 0.6 m3/m3 with steps of 0.1 m3/m3. Thesebin classes are based on wave group averaged concentrations per swash cycle andconsequently, intra wave group concentration fluctuations are still captured (Figure 5.12e,f).For each concentration class, the mean vertical elevation z’ with respect to the wave averagedbed was calculated. In the present experiments the six classes contain about 30 swashrepetitions and it is estimated that the mean elevations have an accuracy of about 1 mm. Thissmall variation explains why occasionally concentrations are found to increase with height.This way of presenting the CCM concentration data was developed for oscillatory sheet flowmeasurements (Ribberink and Al Salem, 1995; McLean et al., 2001) and is especially usefulwhen studying the sheet flow response at various elevations of the sheet flow layer (e.g. pickup layer and upper sheet flow layer).
Another way of presenting the same data is through color contours of the time varyingconcentration profiles (Figure 5.12i,j). Note that for wave A, the concentration profiles inFigure 5.12i corresponds to the profiles in Figure 5.11. Also included in Figure 5.12i,j are thepivot elevation (corresponding to Figure 5.10e,f) and the time varying bottom of the sheetflow layer derived from the ODW04 curve fit.
Typical sheet flow layer pick up behavior, as known from oscillatory sheet flows, can beobserved in the concentration time series (Figure 5.12e,f) at the lowest elevations where theconcentrations are close to 0.6 (packed bed). The concentrations show temporary dips atinstances of sediment pick up from the bed. Deeper dips suggest stronger sediment pick up.This pick up happens once during the uprush (shortly after bore arrival; around t/Tgr = 0.10 forboth swash events) and one or two times during the backwash phase (around t/Tgr = 0.5 and0.65). For swash event A the strongest pick up occurs during the backwash (around t/Tgr =0.65), while for event type B this happens during the uprush. Similar to oscillatory sheet flows,this pick up behavior is observed at low elevations in the bed where the concentrations exceedthe bed water interface value (C > 0.3) and it occurs generally when velocity magnitudes arehigh.
At higher elevations, in the so called upper sheet flow layer (C < 0.3), the concentrationbehavior differs strongly from oscillatory sheet flows. For oscillatory sheet flows in wavetunnels (O’Donoghue and Wright, 2004a) as well as under non breaking surface waves(Schretlen, 2012), sediment exchange occurs between pick up and upper sheet flow layer. Theconsequence of this predominantly vertical exchange is that a concentration dip in the pick uplayer is accompanied by a similar concentration peak in the upper sheet flow layer (mirroringbehavior). Moreover, this sediment exchange occurs around a steady interface elevation whereC = 0.3 (pivot point). In the present swash experiments this type of behavior is not clearlyvisible. Firstly, the pivot level is not steady but fluctuates over a vertical distance of severalmillimeters during the wave cycle (Figure 5.12i,j). Secondly, the present swash experiment
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does not show the mirroring behavior in concentrations during each instance of sheet flow.During the early uprush, the sediment pick up around t/Tgr = 0.1 is not accompanied by anincrease in upper sheet flow layer concentrations. Instead, concentrations drop at all elevationsas a result of the strong bed level decrease (Figure 5.12i,j). During the pick up event in thebackwash (around t/Tgr = 0.65 for both events), concentrations in the upper sheet flow layer areindeed increasing. Although this may point towards vertical sediment exchange (pick up),during the remainder of the backwash the upper sheet flow layer concentrations continue toincrease even though no pick up is observed (t/Tgr = 0.65 to 0.90). These observations arediscussed in more detail in Section 5.7.2.
5.6.3 Particle velocities and fluxes in the sheet flow layer
Particle velocities in the sheet flow layer were calculated following the approach of McLean etal. (2001). This method assumes that (clouds of) particles travel past the co located sensors 1and 2, and the travel time can be found by estimating the phase lag through cross correlatingthe high pass filtered (1 Hz cutoff) signals of the two sensors. This cross correlation is done foreach individual wave and for a selected number of phases of the wave cycle (in this case 100).For each phase, the cross correlation output for all wave cycles is averaged. This averaging isdone per wave averaged concentration bin class, using the same six classes as in Section 5.6.2.For each bin class and phase, the time lag corresponding to the maximum averaged crosscorrelation output is used to estimate the mean travel time of particles between both sensors.Data for which the maximum cross correlation value did not exceed the background noise areemitted. Particle velocities are defined as the distance between both sensors (1.5 cm) dividedby the derived travel time. Figure 5.12c,d shows that particle velocity estimations are onlyobtained when instantaneous ADV velocity magnitudes approach or exceed a threshold ofroughly 1.0 m/s.
Although the measurements show considerable scatter, it is clear that for both swash eventsthe measured particle velocities in the sheet flow layer (Figure 5.12c,d) follow a similar intrawave pattern as the flow velocities measured by the ADV at an elevation of about 3 cm abovethe bed. During both uprush and backwash the particle velocities in the sheet flow layer canreach large magnitudes (1 m/s and higher). Particle velocities in the upper sheet flow layerapproach the near bed water velocity magnitudes, which is not uncommon for sheet flowobservations (e.g. McLean et al., 2001). Vertical structure of the particle velocities is onlyevident for the long backwash of swash event B, with particle velocities decreasing towardsthe bed (in line with observations of McLean et al., 2001; Dohmen Janssen and Hanes, 2005;Schretlen, 2012).
The combination of concentration and particle velocity measurements by the CCM+ sensorsallows us to directly estimate the intra wave horizontal sediment fluxes, as the product of themeasured particle velocities (Figure 5.12c,d) and concentrations (Figure 5.12e,f) per bin class.The horizontal sediment fluxes (Figure 5.12g,h) show a similar oscillating pattern as theparticle velocities. Both swash events A and B show large fluxes during the relatively shortuprush, followed by a longer period with smaller fluxes during the backwash. The magnitudesof the fluxes during swash event B are clearly larger than during event A. Despite the scatter
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Figure 5.12. Phase averaged hydrodynamics and intra wave sheet flow behavior at group period Tgr =15 s for characteristic swash events “A” (left) and “B” (right). (a,b) water level measurements by
AWG, ensemble (grey lines) and mean (dashed black line); (c,d) horizontal velocity measurements byADV, ensemble (grey) and mean (dashed black line), plus CCM+ particle velocities for six
concentration bin classes (colors corresponding to panels e,f); (e,f) concentration measurements C forsix wave group averaged concentration bin classes, including corresponding mean relative elevationsz’ per bin class; (g,h) sediment fluxes derived from CCM+ measurements for six concentration bin
classes; (i,j) contour of concentrations C(z’,t) measured by probe 1/2, including elevations of sheet flowlayer top (solid grey line), pivot point (solid white line), and bottom (dashed black line); (k,l) sheet
flow layer thickness, estimations from ODW04 fit (dots) and spline smoothened estimations (dashedline).
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of the data a general tendency can be seen: the fluxes increase with decreasing elevations inthe sheet flow layer (see e.g. the backwash of wave B). The reduction of velocities towards thebed is more than compensated by the larger volumetric sediment concentrations at theselevels. Note that also for oscillatory sheet flows, highest fluxes were found in the pick up layer(McLean et al., 2001; Dohmen Janssen and Hanes, 2005; Schretlen, 2012).
5.6.4 Sheet flow layer thickness
The thickness was estimated from the interpolated profiles derived from the ODW04 fit(Section 5.6.1). The sheet flow layer thickness ( s) is defined as the distance between the bottomof the sheet flow layer and the level where the volume concentration reaches 0.08 m3/m3
(Dohmen Janssen and Hanes, 2002; O’Donoghue and Wright, 2004a). Hence, the thicknessrelates to the vertical concentration gradients (Figure 5.12i,j and Figure 5.11).Temporal behavior of s (Figure 5.12k,l) agrees with results in previous sections. The thicknessincreases at the previously identified instances of sediment pick up (during early uprush andmid backwash phase; Figure 5.12e,f). There is also a clear correspondence between thick, welldeveloped sheet flow layers, and the derived fluxes (Figure 5.12g,h).The measured maximum s values are substantially higher than observations of oscillatorysheet flow with similar grain size and velocity magnitudes. Tunnel measurements ofO’Donoghue and Wright (2004a) with narrow distributed medium grained sand (D50 = 0.28mm) and peak velocities of 1.5 m/s, yielded maximum sheet flow thicknesses of 8 mm (caseMA5010). Measurements under progressive surface waves in a wave flume (Schretlen, 2012;case RE1575m) yielded sheet flow thicknesses of 10.3 mm for medium grained sand (D50 =0.245 mm) and crest velocities of 1.63 m/s. Compared to aforementioned experiments, peakflow velocities are lower but sheet flow thicknesses during both uprush and backwash areover twice as high. This holds in particular for swash event B.
5.7 Discussion
The new experiments with the CCM+ instrumentation have resulted in new detailed results inthe bed level and sediment (sheet flow) dynamics during swash events in the lower swashzone. In this section, the bed level (Section 5.7.1) and sheet flow (results) are connected toexisting knowledge on sediment dynamics in the swash and to previous observations ofoscillatory sheet flows.
5.7.1 Bed level motions at various time scales
The measured intra group bed levels in the lower swash show a consistent pattern of rapiderosion during the uprush and gradual accretion during the backwash phase. Steep horizontalsediment transport gradients, induced by the strong non uniformity of the waves and flow inthe swash as pointed out for instance by Hughes et al. (2007), may directly lead to these typesof erosion/accretion events. The measurements suggest that the sediment mobilized at the startof the event is transported onshore during the uprush and brought back during the backwash(i.e. cross shore advection). The importance of cross shore sediment advection on swash
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morphology has been addressed before and has been associated to suspended sedimentsettling lags due to enhanced turbulence and hindered settling (Pritchard and Hogg, 2005;Hughes et al., 2007; Alsina et al., 2009). The results further show that the net bed level changeafter a single swash cycle results from a difference between uprush erosion and backwashaccretion, and support the idea that the swash zone bed level change results from a smalldifference of two opposing sediment movements with similar high magnitudes (Masselinkand Hughes, 1998). Our observations for one wave condition do not object reported cases forrandom wave conditions, where a few “large” swash events were responsible for themeasured beach face elevation changes (e.g. Puleo et al., 2014).
Swash events A and B are similar in terms of wave energy, peak onshore and offshorevelocities, and relative durations of uprush and backwash. The modulation of the short wavephase at the repeat frequency triggers different types of specific wave swash interactions, thatare characteristic for the lower swash zone (Hughes and Moseley, 2007). This leads to localdifferences in terms of hydrodynamics (e.g. velocities, turbulence, pressure gradients) whichin return affect sediment transport patterns. Little is known about the effects of wave swashinteractions on bed level changes. Here, effort is made to relate the observations in bed levelchanges to the wave swash interactions observed for both events in a qualitative sense.
The bed level drop during the early uprush for event B is larger than for event A, suggestingsteeper horizontal sediment transport gradients for event B at this instance. The higher sheetflow thickness and fluxes for the event B uprush suggest that this uprush is more energetic, interms of bed shear, horizontal pressure gradients, and/or turbulence (Lanckriet and Puleo,2015). These same factors affect local sediment entrainment by bores (Puleo et al., 2000; Butt etal., 2004; Jackson et al., 2004). The interaction between the two incident bores which form theuprush of event B and which are close in phase at the CCM+ measuring location may partlyexplain why uprush B is more energetic than uprush A. Note that the bed level change is aresult of instantaneous sediment transport gradients, which means that pre suspendedsediment that is advected from the inner surf towards the lower swash zone may also be animportant factor (Jackson et al., 2004; Pritchard and Hogg, 2005).
For event A, strong wave backwash interactions result in a stationary bore at the CCM+
location which seems to promote sediment pick up (Figure 5.12i, t/Tgr = 0.5 to 0.7). Sedimentsuspension events under stationary bores have been observed before (Caceres and Alsina,2012) and relate to strong vertical (turbulent) velocity fluctuations (Aagaard and Hughes,2006). Accretion of the bed starts a couple of seconds after the incident bore arrives at themeasuring location, and is possibly explained by a decrease in velocities and sediment settlingas a result of the backwash interruption (Puleo et al., 2014). For event B, the combination ofstrong accretion and high near bed sediment concentrations during the mid final backwashstage suggests a large amount of advected sediment arriving from the shoreward direction(i.e. a larger amount than for event A). This large amount of sediment is possibly mobilized bythe stationary bore that was observed about 1 m shoreward from the CCM+ location for eventB.
The sequence of the various erosion and accretion events induced by the individual wavegroups forms an overall bed level fluctuation at the repeat period TR (= 195 s). This slow bedlevel fluctuation is of similar magnitude (1 2 mm amplitude) as the net bed level change
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induced by each swash event (2 3 mm), which suggests that both are potentially relevant forswash zone morphology. To the authors’ knowledge, only one study discusses the effects ofthis repeat frequency on near shore processes. Baldock et al. (2000) report the potentialrelevance of wave phase modulations at the repeat frequency on the generation of wavebreakpoints and on water surface levels and run up in the swash. Similar to Baldock et al.(2000), the low frequency regions in our experiment show negligible energy in the water levelspectrum (Figure 5.5f) and the wave groups are approximately equal in terms of wave energy.This suggests that the bed level changes occurring at fR are the result of sediment transportprocesses repeating at this repeat frequency, e.g. processes driven by wave swash interactionsduring uprush and backwash, rather than the result of water surface oscillations associated tothis frequency. A spectral coherence analysis between bed levels (CCM+) and water surfacelevels (AWG) for these data supports this explanation, showing minor energy at fR comparedto the values at fgr (Alsina et al., 2014). This marks a clear difference from previous studies thathighlighted the importance of low frequency (infra gravity) waves on swash zone sedimenttransport processes (Beach and Sternberg, 1991) and bed level changes (Puleo et al., 2014), asthese studies found substantial energy in the low frequency bands of the water level spectrum.
The present results highlight the importance of wave swash interactions on bed level changesand swash morphology. However, a more thorough explanation of the observed local bedlevel changes requires a characterization of bed level changes and sediment transport ratesalong the complete swash zone. Moreover, bed level measurements for a wider range of swashconditions (e.g. including uprushes and backwashes that are free of interactions) are requiredfor a more generic assessment of the importance of these interactions.
5.7.2 Sheet flow dynamics and implications for modeling sheet flow transport in the swashzone
Sheet flow transport is observed at instances with sufficiently high instantaneous velocities (>1 m/s), which agrees with observations of oscillatory sheet flows (O’Donoghue et al., 2006).These instances occur mainly during the uprush and during the middle/final stage of thebackwash phase, which agrees with earlier observations for natural swash zones (Yu et al.,1990; Lanckriet et al., 2013; Lanckriet et al., 2014). The dynamics of the sheet flow layer for thelower swash in this experiment exhibit both similarities and differences with oscillatory sheetflow. Differences are attributed to (i) effects of bore induced turbulence and (ii) the importanceof flow non uniformity and horizontal advective transport.
At the lowest vertical elevations, the pick up of sediment during the wave group shows astrong similarity with the pick up occurring in oscillatory flows (also surface waves). Pick upevents occur predominantly at instances of large horizontal velocities and accelerations(during uprush and backwash) and can probably largely be explained by horizontal shearinduced turbulence (see e.g. Kranenburg et al. 2013). However, in line with Lanckriet and Puleo(2015), our results indicate that not only horizontal shear but also bore turbulence can promotesediment pick up and sheet flow layer growth. This is observed firstly for the early uprush(t/Tgr = 0 to 0.1) of both events, where pick up is major and sheet flow thicknesses are higherthan for oscillatory sheet flow studies with similar sediment and peak velocities, and secondlyfor the backwash, where the stationary bore at the CCM+ location for swash event A (from t/Tgr
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= 0.6 to 0.8) promotes vertical sediment exchange even though water and particle velocities arelow.
During the backwash, the local bed slope may promote the mobilization of sediment.However, the absence of sediment pick up during the final backwash stage suggests that thehigh near bed sediment mass is not locally entrained (vertical exchange) and must thereforebe arriving from the middle/higher swash (horizontal advection). The accretion of the bedduring the backwash supports this idea of a large amount of advected sediment arriving fromthe onshore direction. This large transport is confined to a small water layer, so sedimentconcentrations are likely of similar magnitude as concentrations restricted to upper sheet flowlayers for oscillatory flow conditions. As a result, the sheet flow layer thickness during thebackwash of both events is larger than expected based on local hydrodynamics and previousobservations for oscillatory sheet flows. This is in particular true for event B, where backwashsediment advection is likely higher (see Section 5.7.1), resulting in a large sheet flow thickness.
The new measurements show that cross shore sediment advection in the swash is not onlyrelevant for suspended sediment transport, but it also affects the characteristics of the sheetflow layer. Consequently and unlike previous observations for oscillatory sheet flow, the sheetflow dynamics and fluxes during uprush and backwash are not purely controlled by localhydrodynamics. This implies firstly that vertical profiles of particle velocities and fluxes donot necessarily scale to sheet flow thicknesses: sediment fluxes may be low even when sheetflow thicknesses are high (e.g. below stationary bore during event A backwash). A secondimplication is that ‘local’ formulations for sheet flow sediment transport of the type of MeyerPeter & Mueller (e.g. Nielsen, 2006) may not be valid for the swash zone. Instead, sheet flowtransport models for the swash may require a coupling with an intra wave advection diffusionmodel that calculates time dependent near bed suspended sediment transport (such as Alsinaet al., 2009; Zhu and Dodd, 2015). On the other hand the measurements showed that (i)especially the upper sheet flow layer is influenced by advection effects – the pick up layer stillshows a strong resemblance with oscillatory sheet flows; (ii) the largest sheet flow fluxes seemto occur in the lower parts of the sheet flow layer. Therefore, characteristics of the sheet flowpick up layer may still be locally controlled, and sand transport in this layer could be modeledas such.
5.8 Conclusions
Measurements of bed level fluctuations and detailed sheet flow characteristics throughout acomplete swash cycle are presented. These measurements were obtained in the lower swashduring a wave flume experiment involving bichromatic wave groups. A new instrument(CCM+), capable of measuring continuous gradual bed level evolution as well asconcentrations and particle velocities in the sheet flow layer, was applied for the first time.
At the lower swash location studied here, observations of the CCM+ system show a consistentpattern of rapid net bed erosion during the early uprush and gradual accretion during themiddle backwash phase. Subtle differences in hydrodynamics between the various wavegroups lead to substantial differences in both the magnitude of the intra group bed levelfluctuations (6 13 mm) and in the net bed level change (2 3 mm erosion or accretion) induced
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by each group. This causes the bed to respond not only at the group frequency of thebichromatic waves, but also at the repeat frequency of the wave group sequence.
Sheet flow transport was observed at the early uprush and during the middle and latebackwash phase. At the early uprush, the growth of the sheet flow layer and the drop in bedlevel occur almost simultaneously. The sheet flow layer exhibits some features similar tooscillatory sheet flow, such as sediment entrainment from the pick up layer. This pick up isobserved not only when horizontal shear velocities are high, but also in occurrence of waveswash interactions during the backwash. Direct cross shore sediment flux measurements inthe sheet flow layer from the CCM+ show similarities with oscillatory sheet flow conditions,with highest flux rates found in the pick up layer.
Notable differences from observations of oscillatory sheet flow are (i) a time varying elevationof the concentration pivot point within a wave group cycle; (ii) an absence of mirroringconcentration behavior in pick up layer and upper sheet flow layer. These differences can beexplained from the highly non uniform flow conditions. Sediment advection dominates theupper sheet flow layer concentration behavior and the properties of the sheet flow layer arenot fully locally determined. This implies that existing ‘local’ formulations for sedimenttransport may not be valid for the swash zone.
5.A. Evaluation of CCM+bed level measurements
The new concentration tracking system is in essence a feedback loop between concentrationsand sensor movement, ensuring that the sensor will always move in the direction of a certaintarget concentration. If the tracking system would perform ideally, the system would be ableto keep the measured concentrations at all times at a target value through continuousadjustment of the sensor elevation. In practice, the probe fluctuates around the elevation of thetarget concentration. This is due to (i) the limitations of control system (e.g. system lags andprobe risks overshooting); (ii) the spiky nature of the measured concentration signal; (iii) thetime varying vertical concentration gradients. As a result of the latter, there is not a singleperfect setting for the tracking system’s gain factor for an experiment, as the responsesensitivity (in terms of vertical distance to be covered for a certain measured concentrationoffset) should be constantly varying.This section evaluates the performance of the new concentration tracking system. This is donein two ways: (i) by studying the probe’s tracking ability in the spectral domain (Section 5.A.1);(ii) by comparing the phase averaged intra group bed level measurements of the ‘quick’ CCM+
probe 3 with bed level estimations obtained from the CCM+ probe 2 concentrationmeasurements (Section 5.A.2). The results are evaluated in Section 5.A.3.
5.A.1 Evaluation of CCM+ in the spectral domain
As a start, the probe’s response at various time scales is analyzed. Rather than examining thetime series of the probe, the power spectra of concentrations and positions of the various CCM+
probes are studied. In order to explain this, consider a first case of a fixed probe at a constantlevel near the bed interface (so no bed level tracking). This probe measures concentration
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fluctuations as a result of sheet flow behavior or bed level motions. The various types offluctuations will appear as energy peaks in a power spectrum of the measured concentrations.Now consider a second case of an ideally tracking probe, i.e. the probe is able to keep up withall elevation changes necessary to keep the measured concentration constantly at its targetvalue. In this situation the power spectrum of the (constant) concentration signal will not showany energy, while on the other hand the power spectrum of the probe elevation will showenergy peaks at the dominant physical frequencies. In practice, the probe control system is notideal, and it can be expected that especially the high frequency fluctuations of the bed cannotbe followed by the probe. Consequently, these frequencies will not appear in the powerspectrum of the probe elevation but will appear in the power spectrum of the concentrationsignal instead.
Figure 5.A.1. Power spectral densities of concentrations (upper) and positions (lower) for ‘slow’ probe2 (left) and ‘quick’ probe 3 (right). Data of one run in semi equilibrium conditions.
Power spectra of concentrations and positions for both probes are found in Figure 5.A.1.Concentration measurements of probe 2 show distinct peaks at fgr (0.067 Hz) and 0.5fgr, and asmaller peak at fR (0.005 Hz). Physical explanations of these peaks are given in Section 5.1.Spectral energy of this probe’s position is restricted to the lower frequency bands, with a clearpeak at fR. This suggests that probe 2 moves with the lower frequency bed level motions, butit is at an approximately fixed level at frequencies higher than 0.01 Hz. At these higherfrequencies, the probe measures concentrations while being at a close to fixed position – so itsmovements do not distort the measurement.Probe 3 shows a reverse pattern. As expected, the total energy in the concentration spectrumis less than for probe 2, while there is more energy in the position spectrum. The concentrationspectrum shows negligible energy at frequencies lower than fgr. Apparently, in this lower
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frequency range, the probe is able to keep concentrations constantly at its target value, i.e. theprobe is well able to follow bed level evolution. The peak in the concentration spectrum ofprobe 3 at fgr indicates that the probe is not able to respond perfectly to bed level changesdriven by the wave groups. The spectral energy of this peak in C is much smaller for probe 3than for probe 2, which suggests that the probe approaches but not perfectly tracks the intragroup bed level.Based on these results in the present swash experiments, CCM+ probe 3 is only used to providebed level (reference) information at time scales larger than the wave group time scale(frequencies < 0.067 Hz). CCM+ probe 2 is used to provide concentration information at timescales equal to or smaller than the scale of individual wave groups (f > 0.067 Hz).
5.A.2 Evaluation of the CCM+ bed level tracking system in the time domain at short (intrawave group) time scales
Figure 5.10e,f can be used to compare the phase averaged intra group bed level measurements(CCM+ sensor 3) and the pivot elevation extracted from the concentration measurements(sensor 2). The latter approaches closely the real bed, as it should not be experiencing anyphase delay.
Qualitatively, the intra wave bed measurement (probe 3) resembles the actual pattern of pivotlevel fluctuations. It is obvious that the magnitudes of the intra group bed level measurementsby probe 3 (4 and 6 mm for events A and B, respectively) are smaller than the observed pivotpoint fluctuations (event A: 6 mm; event B: 13 mm). In addition, the bed level measurementsof probe 3 lag the pattern of the “real” bed with a delay up to about 2 s. This is most evidentduring the uprush phase where erosion is severe. Apparently, the probe is not able to followthe bed when it evolves rapidly on a time scale of 1 to 2 s.
5.A.3 Discussion of CCM+ capabilities
The CCM+ in quick tracking mode is well able to track the bed at frequencies lower than fgr(0.067 Hz) in the present swash experiment. At frequencies similar to or higher than fgr, thequality of the CCM+ measurement decreases. On an intra group time scale the CCM+ bed levelmeasurement shows a smoothened and lagged representation of the actual bed. Thissmoothening and lagging depends on the magnitudes and time scales of the erosion andaccretion events that induce the bed level fluctuations. E.g. for swash event A, characterizedby a less severe erosion/accretion pattern than event B, the direct bed level measurement ofCCM+ is of better quality.
The CCM+ probes are physically able to move substantially faster than during the currentexperiment. The gain factor that controls the probe’s movement sensitivity can be increased.However, this soon results in probe overshooting and unstable behavior, in particular whensheet flow layers are small or absent (i.e. when there is a direct vertical transition from theimmobile bed to ‘clear’ water). The CCM+ tracking capabilities can possibly be improved byincluding more sophisticated proportional integral derivative (PID) control loops. However,for experiments with repeating wave conditions as reported herein, the main purpose of the
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CCM+ bed level tracking system would be to measure the gradual erosion patterns only;something the measuring system is well capable of.
As discussed in the introduction, most of the ‘classic’ instrumentation (e.g. echo sounders) failsto measure the bed during both exposed stages and submerged stages of the bed. In terms ofconcentration measurements, most instruments (e.g. OBSs) fail at measuring the highconcentrations during the early uprush and late backwash phase when water depths areshallow. The recently developed Conductivity Concentration Profiler (CCP; Lanckriet et al.,2013) is the only instrument capable of measuring sheet flow concentration profiles and bedlevel changes with high temporal (f > 1 Hz) resolution. The CCP measures a complete sheetflow concentration profile at once, which is a major advantage in many conditions. However,it also has limitations, e.g. (i) sheet flow thicknesses smaller than 3.5 mm cannot be resolved(Lanckriet et al., 2013); (ii) the measuring window (30 mm) is limited, which may lead to asubstantial loss of data when the bed is evolving (Puleo et al., 2014); (iii) the system is unableto measure particle velocities. Regarding the latter, it is stressed that to the authors’ knowledgenone of the existing instrumentation but the CCM+ is capable of direct particle velocitymeasurements. Yet, these measurements are of crucial importance for estimation of sedimentfluxes and understanding of swash morphology.
Obvious limitations of the CCM+ system are (i) it cannot directly measure rapid instantaneousbed level changes; (ii) it provides a point measurement of concentrations (and not a completeprofile). As a result, phase averaging is required to sample the complete sheet flow layerincluding time varying bed levels during a wave (group). More of practical nature is the factthat the dimensions and weight of the tank make it an instrument more suitable for laboratorythan field conditions.
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6 DiscussionThis Discussion chapter first reflects on the research methodology as followed in this thesis(6.1) and then on the possible implications of the new results for improving engineering typesand transport models (6.2).
6.1 Methodology
This section addresses the choices made in the experimental design and the extent to whichthese choices affect the results. Specifically, the section addresses general uncertainties relatedto the wave flume experiments (6.1.1), scale effects (6.1.2), the choice of wave conditions (6.1.3)and instrumental limitations and uncertainties (6.1.4).
6.1.1 Experimental constraints
The main advantages of wave flume experiments are that processes can be isolated and thatwave conditions can be controlled and repeated. This for example enables ensemble averagingover many wave cycles to improve confidence in the results (see also Section 1.5). In addition,the experiments are fully reproducible. However, there are also drawbacks of suchexperiments. These drawbacks are extensively discussed by Hughes (1993); the mostimportant ones for the present study are shortly addressed in this section.
Flume seiching generated a standing long wave with period of about 45 s and amplitude ofO(cm), which was identified from the spectra and was filtered out prior to the analysis ofvelocities (Chapter 2). Waves in the CIEM flume were generated based on first order theory,which leads to the generation of ‘spurious’ free long waves that interact with the short waves(Barthel et al., 1983). In addition, short waves were reflected by the bar slope and bar and bythe not fully dissipative fixed beach. Both effects (spurious waves and reflection) induce crossshore modulations in wave statistics (wave height, skewness, asymmetry), particularly alongthe offshore slope of the bar (c.f. Van der A et al., Submitted). The modulations in wave heightwere of O(cm) and were considered negligible relative to changes induced by wave shoalingand breaking. Higher order wave statistics (skewness, asymmetry) may be more significantlyaffected by spurious and reflected waves, and this in return affects cross shore varyingsediment transport rates (c.f. Chapter 4). Unfortunately, the dynamic pressure measurementsdid not enable detailed examination of the wave shape deformation. Note that the cross shorevariation in near bed velocity and acceleration skewness is qualitatively consistent withobservations of water surface levels (Flick et al., 1981; Beji and Battjes, 1993). Therefore, it isconcluded that wave deformation is largely explained by shoaling, breaking and de shoaling,and that effects of spurious and reflective waves are inferior.
The flow in the wave flume is two dimensional (x, z) by approximation: transverseasymmetries in flow and in sediment transport did appear. Circulations in the x y plane wereconfirmed by accompanying experiments (Van der A et al., Submitted) and are possibly
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explained by an imbalance in flow perturbation by the measuring instrumentation at eitherside of the flume’s centerline. This circulation is not expected to importantly affect the nearbed measurements, since the ACVP was deployed close to the center of the flume, but it maylead to a slight offset (<0.05 m/s) in ADV measured time averaged velocities at outer flowelevations. In addition, the bed profile was not fully symmetric; instead, the bed wasconsistently lower at the flume’s side walls and higher along the flume’s centerline. This wasparticularly true at inner surf zone locations during the breaking wave experiments. The bedasymmetry may be caused by circulations in the y z plane or by scouring at the flume’s sidewalls. For the swash experiments (Chapter 5), bed asymmetries were levelled out after every2 hours of experimental duration. For the breaking wave experiments (Chapters 2 to 4), a 3 Dscan of the bed profile was obtained using a sand ripple profiler after finishing one of theexperimental repeats. The scan showed that although transverse asymmetries were evident,the transverse averaged bed profile was close to bed profile measurements obtained from oneof the acoustic bed level sensors (the sensor deployed about halfway between the flume’scenterline and flume side walls). Therefore, bed levels used for further analysis were at innersurf zone locations based only on this sensor, while the bed at other locations was taken as themean of both sensors.
Most instruments were deployed in situ. The mobile frame and wall frames holding theinstrumentation were designed to be sufficiently stiff to withstand the impact of wave forcing.The natural frequency of the mobile frame was checked through accelerometer testing prior tothe breaking wave experiments. During the experiment, auto spectra of velocities did revealsmall peaks at the frame’s natural frequency (around 10 Hz), but the associated energy wasorders of magnitude smaller than the energy contained in the physical turbulence. The in situdeployment of the instruments plus frames further led to flow interference and possible waketurbulence. The effects of wake turbulence were assessed using the most offshore location asa reference, as physical turbulence due to waves and currents is small at this location. No cleareffects of wake turbulence on the ACVP data were found (Chapter 2). Accompanyingexperiments by Van der A et al. (Submitted) revealed, through inter comparing turbulenceintensities by two separate instruments, a local increase in outer flow turbulence intensity byADVs due to wake turbulence induced by the measuring frame. However, the turbulentvelocity fluctuations associated with such wake turbulence are of O(0.01 m/s) and are onlysignificant far from the breaking region where other sources of turbulence are minor.
The research in Chapters 2 to 4 involves complex interactions between various hydrodynamicand sediment transport processes. Due to these interactions it is not always trivial to explainthe physical processes based on the experimental observations alone. This is for example truefor combined bed slope and breaking generated TKE effects on wave bottom boundary layerthickness (Chapter 2) and on bedload transport rates (Chapter 4). Further experiments thatisolate such processes, or simulations with process based numerical models, can help tofurther advance the understanding of sediment transport physics in the surf and swash zones(Section 7.2).
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6.1.2 Scale of experiments
The scale of the breaking and swash zone experiments does not differ much from field scale.The median sediment diameter (D50) of 0.24 mm in the experiments is close to the typical size(D50 = 0.25 mm) found on Dutch shorefaces (Van der Spek and Lodder, 2015). Results for thebreaking zone (Chapters 2 to 4) are based on regular waves with period T = 4.0 s and ‘offshore’wave height H0 = 0.85 m. These waves are of slightly smaller period/height than reportedaverage wave conditions near the Dutch coast (c.f. Wijnberg and Terwindt, 1995; Grasmeijer,2002) (yet still considerably smaller and shorter than reported swell waves, c.f. Ruessink, 2010).Offshore wave heights for the swash zone experiments (Chapter 5) are substantially smallerthan waves at Dutch coasts, but the wave conditions result in cross shore velocity magnitudesin the swash zone that are similar to field observations (c.f. Chardón Maldonado et al., 2015).
As the experiments are near full scale, the sediment properties were not scaled. The largescale waves led to Reynolds numbers and turbulence properties that are similar to field scalesover the complete water column including the wave bottom boundary layer. The importanceof such large scale conditions is best illustrated by comparing the temporal turbulencebehavior. In small scale laboratory studies with plunging waves, breaking generated TKErapidly saturates the water column and dissipates almost completely before the end of thewave cycle, leading to a strong temporal variation in TKE (e.g. Ting and Kirby, 1995; De Serioand Mossa, 2006). However, in the present experiments, the temporal variation in TKE is muchsmaller; TKE builds up over multiple wave cycles since a large fraction of breaking generatedturbulence persists into the subsequent wave cycle (c.f.Chapter 2; Van der A et al., Submitted).Van der A et al. (Submitted) argue that this difference is purely due to the scale of theexperiments: the ratio between the largest and the smallest turbulence length scale increaseswith Reynolds number (e.g. Pope, 2000) and this ratio is therefore much higher in a full scaleexperiment. Consequently, in a larger scale experiment, the largest turbulent vortices requirea longer duration to fully dissipate.
Drawbacks of such large scale experiments are that instruments have to be deployed in situ(see also previous section). This differs from small scale wave flume experiments, wherehydrodynamics can be measured more easily with ex situ optical instruments that do notdisturb the flow (e.g. LDA, PIV). Another advantage of small scale experiments is thatinstruments such as PIV can instantly measure the two dimensional velocity field with highspatial resolution; in large scale conditions, the existing instrumentation requires manyexperimental repeats to obtain a high spatial coverage of measurements. The in situdeployment further requires a very carefully designed experimental set up, in order to obtainsuch high resolution (mm scale) measurements without flow blocking or instrumentalvibrations. Especially the measuring frame requires a careful design and often needs to becustom built for the experimental purpose. Other constraints of large scale experiments aremore of practical nature: (i) the restoration of bed profile is a laborious exercise; (ii) a significantportion of the experimental time gets lost in the draining and filling of the flume; (iii) a teamof 4 5 persons is required to conduct the experiments. These practical constraints explainpossibly why such few datasets of sand transport process measurements under large scalewave conditions are available.
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6.1.3 Wave conditions
An important limitation in the present thesis is the limited number of experimental conditions.The experiments were designed primarily for obtaining new insights in sediment transportprocesses. However, different wave conditions would have resulted in differences in terms ofhydrodynamics which in return would alter sediment transport processes. For instance, twoimportant wave parameters controlling turbulence and sediment dynamics in the breakingregion are the breaker index (H/h) and the breaker type (plunging, spilling). The breaker indeximportantly controls time averaged turbulent kinetic energy in the water column (Ruessink,2010) and, in return, sediment entrainment (Steetzel, 1993). The breaker index also correlatespositively with wave asymmetry, and consequently, with near bed velocity and accelerationskewness (Grasso et al., 2012). The breaker type affects the vertical distribution of TKE, withstronger mixing and a larger penetration depth of breaking generated turbulence underplunging than under spilling breakers (e.g. Ting and Kirby, 1994). This leads to significantdifferentiation in terms of sediment entrainment and mixing between both breaker types(Aagaard and Jensen, 2013). Both breaker types differ notably in terms of TKE transport andproduction/dissipation, resulting in stronger temporal variability in TKE for plunging than forspilling breakers (Ting and Kirby, 1994). In return, the spatiotemporally varying TKE affectssuspended sediment transport (e.g. Chapter 3). Section 3.5 discusses how other waveconditions may lead to different behavior in spatiotemporally varying TKE and in suspendedsediment transport.
These studies show that the results in the present experiments will not be valid for the fullspectrum of wave conditions at natural beaches. At the same time, the present study (with alarge spatial coverage of measurements for a limited number of wave conditions) allows amore in depth analysis of the cross shore variation in sand transport processes than most ofthe previous studies (that involved varying wave conditions but limited spatial coverage).Both approaches yield different insights in cross shore sand transport processes in the surfand swash zones.
Non breaking wave studies have shown how sediment processes and transport rates greatlydepend on sediment diameter, with finer sediment leading to suspension at higher elevationsand exhibiting phase lags that may alter the direction of time averaged sediment fluxes(Dohmen Janssen et al., 2002; O Donoghue and Wright, 2004b). Compared to the presentmedium sand experiments, where near bed vertical concentration gradients are steep andwave related suspension remains largely confined to the wave bottom boundary layer,experiments with finer sand or larger waves could lead to substantial differences in terms ofsediment entrainment and vertical distributions of sediment fluxes. Specifically, highercontributions of (current related and wave related) suspended transport relative to bedloadtransport may be expected for finer sediment/larger waves.
The choice for regular (monochromatic) waves leads to higher time averaged velocities(undertow magnitudes) than for equivalent irregular waves (Ting, 2001). The undertow in thebreaking region dominates net transport of TKE (Van der A et al., Submitted) and of suspendedsediment (Chapter 3). In field conditions, where waves are irregular, one would find lessstrong undertow magnitudes (c.f. Garcez Faria et al., 2000) and a lower relative importance ofcurrent related suspended fluxes to total suspended load (c.f. Ogston and Sternberg, 1995;
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Ruessink et al., 1998). The monochromatic waves further lead to strong cross shore gradientsin transport rates as energetic waves continuously break at the same location. Consequently,the evolving breaker bar is much sharper crested and has steeper bed slopes than bars onnatural medium sand beaches (c.f. Gallagher et al., 1998). Hence, bed slope related processes(e.g. bedload transport) are likely more important in the present study (Chapters 2 to 4) thanin a natural situation.
Altogether, it is recommended to validate the breaking wave results in the present study(Chapter 2 to 4) for a wider range of (combinations of) wave conditions, bed profiles, andsediment sizes (see also Section 7.2).
The swash zone experiment (Chapter 5) was, analogous to the breaking wave experiment,designed primarily to extend insights in sediment transport processes for a specific wavecondition rather than in transport rates or morphology for a wider range of conditions. Thewave condition was designed to result in energetic flow (high onshore/offshore velocities) andstrong wave backwash interactions in the lower swash zone. Such interactions are commonfor natural beaches and have been described by many studies (see Chapter 5, or ChardónMaldonado et al., 2015, for an overview). Chapter 5 illustrates that wave swash interactionsaffect local pick up and can alter sediment transport gradients, inducing local accretion of thebed. The magnitudes of pick up, bed changes, and horizontal advection processes dependshighly on the wave conditions: even very subtle differences in offshore wave conditions maylead to large quantitative differences in sheet flow thickness and bed level changes in theswash zone (Chapter 5). Note further that sediment transport in the swash zone is notdetermined fully locally, but also by the time varying sediment exchange with the inner surfzone (c.f. Alsina et al., 2012). Moreover, transport in the swash is not only due to a (quasi)instantaneous response to local hydrodynamic forcing: instead, particles that are mobilizedas bedload during the backwash phase may be entrained as suspended load upon the start ofthe subsequent swash event (Sou and Yeh, 2011; Pujara et al., 2015b). Due to these three factors(sensitivity to hydrodynamic forcing, not only locally determined, response not fullyinstantaneous), quantitative results in Chapter 5 depend greatly on the chosen bed geometryand (combination of) wave conditions. However, it is expected that sediment processesidentified in Chapter 5 are qualitatively representative for a wider range of swash conditions(i.e. energetic swash events with strong wave backwash interactions at a medium grainedintermediate state beach).
6.1.4 Instrumentation
For the breaking wave experiments (Chapters 2 to 4) the spatial coverage and temporalresolution of the velocity and concentration measurements in the present experiments werelarge compared to previous studies. This is particularly true for the lowest 0.10 m of the watercolumn, a region including the wave bottom boundary layer (WBL) and the sheet flow layer.A higher spatial coverage at outer flow elevations would have been useful in terms ofunderstanding the full extent of spatiotemporally varying hydrodynamics (includingturbulence) and in order to arrive at more reliable estimates of depth integrated suspendedtransport (Chapter 3), which in return would also improve the indirect estimates of bedloadtransport (Chapter 4). However, a higher coverage could not be achieved during the present
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study as (i) adding more instruments to the frame was no option due to the potential risk offlow blocking; (ii) the labor intensive experimental procedure (draining flume, restoringprofile, filling flume) did not allow coverage of more cross shore positions. Instead, the outerand inner flow velocity and turbulence field were sampled with higher spatial (vertical +horizontal + temporal) resolution during a separate campaign, for which the bed was fixed bycovering it with a concrete layer (Van der A et al., Submitted).
Highest near bed TKE, and consequently the most prominent effects of breaking generatedturbulence on sediment transport, is found along the steep shoreward facing bar slope.Unfortunately, no detailed measurements of the bedload layer were obtained at this location.Consequently, the experiment does not provide full insights in how the bedload transportlayer is affected by breaking generated turbulence and by the dynamic vertical sedimentexchange with the suspension layer. This knowledge gap may be filled through additionalexperiments whilst measuring the sheet flow layer with the CCM+, although one should beaware that the rapid local bed level evolution at this location will make it extremelychallenging to obtain high quality measurements of the sheet flow layer.
In addition to the Transverse Suction System (TSS) measurements of time averagedconcentrations, outer flow time varying sediment concentrations were also measured withhigher spatial resolution using an Aquascat Acoustic Backscatter System (ABS) deployed fromthe mobile frame. However, these ABS data had to be discarded due to substantial signalattenuation by air bubbles. Data of two OBSs at the middle and top of the water column werediscarded for the same reason. This shows that one should be cautious with optical andacoustic sand concentration measurements acquired in the bubbly breaking region; the datamay be invalid and should ideally be validated with reference measurements that areinsensitive to air bubble presence (e.g. TSS).
A prototype Acoustic Concentration and Velocity Profiler (ACVP) was applied to measurenear bed hydrodynamics (Chapter 2) and sediment dynamics (Chapter 3). The data of theACVP formed an important basis for the present study, but some concerns are raised here.Firstly, the combination of instrumental limitations and necessary data treatment steps leadsto an underestimation of physical (vertical) turbulent fluctuations, particularly at elevationsvery close (<1 cm) from the bed. This drawback is extensively discussed in the Appendix toChapter 2. Secondly, it should be noted that the acoustic inversion (from acoustic backscatterintensity to sediment concentration) based purely on theoretical considerations (followingroutines of Thorne and Hurther, 2014) did not yield physically meaningful concentrationdistributions (see Chapter 3). Despite ongoing work on acoustic scattering theory (see Thorneand Hurther, 2014, for an overview), one should be cautious when interpreting acousticallymeasured concentrations that have not been compared against reference measurements (e.g.TSS). Thirdly, the vertical bin size of the ACVP measurements (1.5 mm) was, given the ratherthin sheet flow layers and small intra wave bed level fluctuations (O(mm), see Chapter 4), toocoarse for studying the bedload/sheet flow layer. The bin size is limiting here, as the ACVPseems physically capable of sampling the (upper) sheet flow layer when this layer is thicker(e.g. when using light weight particles, see Revil Baudard et al., 2015). The performance of theACVP is yet to be assessed for well developed sheet flow conditions with real sediment.
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Sheet flow layers that are very thin or that occur in very shallow water (i.e. in the swash zone)cannot be studied using present acoustic instrumentation. For such conditions, novelconductivity based instruments such as the CCM+ (Chapter 5) and the CCP (Lanckriet et al.,2013) can measure the high sediment concentrations over the region where acousticinstruments are unsuccessful. However, the quantification of bedload transport rates usingthese instruments remains extremely difficult. The CCP cannot provide velocities in the sheetflow layer and relies on semi empirical models for velocity distributions inside the sheet flowlayer to quantify fluxes (Puleo et al., 2016). The CCM+ can measure particle velocities, but onlyduring a fraction of the wave cycle with sufficiently developed sheet flow thickness and for asignificant amount of wave repetitions (Chapter 5). In the present study, these measuringconstraints hampers not only the estimates of bedload transport, but also the understandingof processes such as sheet flow pick up behavior, the effects of external turbulence, and thecoupling between suspended and bedload transport. Additional experiments or simulationswith detailed process based numerical models may elucidate on these research topics (see alsoSection 7.2).
The swash zone experiments showed continuous erosion and accretion at various time scales,which could for the first time be quantified using the new CCM+ system (Chapter 5). Althoughthe observation itself is interesting and sheds new light on beach response to grouped waves,the measurements do not address whether the bed level changes are induced primarily bybedload or by suspended load transport gradients, and whether the bed changes in the lowerswash zone at the ‘repeat period’ are due to sediment exchange between the lower swash withthe inner surf zone or by an exchange with the upper swash zone. The understanding of swashmorphology would benefit greatly from combined detailed measurements of bed levelchanges and time varying transport rates at adjacent locations (see Section 7.2). Forunderstanding the importance of sheet flow transport for swash morphology, these transportrates should ideally be separated into a bedload (sheet flow) and suspended load contribution.However, as stated in the above, the quantification of bedload transport rates using presentinstrumentation is very challenging.
6.2 Implications for morphodynamic modeling
This section addresses how the insights obtained from the experiments can lead to improvedformulations in engineering type morphodynamic models. Some possible improvements arealso suggested in the discussions sections in Chapters 2 to 5; the present section focuses ontopics that have not been covered in these chapters.
6.2.1 Wave averaged approach in morphodynamic models
Engineering type morphodynamic models operate at a wave averaged time scale to reducecalculation times. Total sediment transport is commonly calculated through a combination ofa wave averaged advection/diffusion model for suspended sediment transport andparameterizations of intra wave sediment transport processes (i.e. wave related mixing,wave related suspended transport, bedload transport). The present study generally supports
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such a wave averaged approach for modeling morphology in the surf and swash zones,although some adaptations may be required (see next sections).
One concern raised here is the parameterization of intra wave velocities, which provides thehydrodynamic input for bedload transport models. Intra wave velocity parameters (e.g. peakonshore and offshore velocity, velocity and acceleration skewness) are predicted throughempirical parameterizations (e.g. Ruessink et al., 2012). Figure 6.1 shows a comparisonbetween measurements and predictions of the near bed velocity and acceleration skewness.Measured skewness and asymmetry vary strongly across the breaker bar. These cross shorechanges in wave shape are likely due to complex behavior of higher order wave harmonics aswaves break and de shoal along the shoreward slope of the breaker bar (c.f. Flick et al., 1983;Beji and Battjes, 1993). Furthermore, as the wave breaks, it splits into a newly reformed surfbore and a secondary crest (Chapter 2). The parameterization by Ruessink et al. (2012) doesnot properly capture these cross shore variations (Figure 6.1). A likely explanation is that theparameterization is calibrated for a wide range of shoaling to inner surf zone conditions but itdoes not account for complex local wave deformation in the breaking region.
Figure 6.1. Velocity skewness (a) and asymmetry (b) around breaker bar: measurements by ADV at0.11 m (squares) and predictions based on local Ursell number following Ruessink et al. (2011)
(dotted line) for t = 0 15 min. Definitions for skewness and asymmetry are found in Chapter 2 and 4.Panel c shows the bed profile at t = 0 min.
It is further seen that the parameterization predicts the magnitudes of skewness reasonablywell (Figure 6.1a), but it significantly underestimates the magnitude of the velocity asymmetry(Figure 6.1b). A possible explanation for the underestimated velocity asymmetry is that thepresent study involves monochromatic waves. Field conditions are different in that (i)interaction between irregular short waves (and interaction with long waves) will likelypromote breaking of the steepest wave in a sequence, hence resulting in a lower waveasymmetry; (ii) the parameterization is based on data that were time averaged (over 15 min.sampling intervals) and bin averaged (over Ursell number classes) and these averaging stepslikely result in smoothening of local maximum values. The uncertainties in predicted
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skewness/asymmetry values hamper predictions of bedload transport rates in the breakingregion, as shown by Schnitzler (2015) using the present study’s measurements in combinationwith Delft3D as a research tool.
To what extent time averaged velocities near the bed are affected by the large penetrationdepth of breaking generated turbulence (Chapter 2) cannot be concluded from the data. Moredetailed analyses with process based numerical models are required to verify whether theapplied formulations for time averaged velocities are appropriate. Specifically, the datapresented here can be used to verify whether near bed time averaged velocities can beadequately modeled using morphodynamic models. Schnitzler (2015) showed that Delft3Dcan qualitatively predict the cross shore variation in undertow velocity for the presentexperiment, but the model underestimates undertow magnitudes by up to a factor 2 and itcannot always capture the vertical structure in the undertow profiles.
6.2.2 Turbulence in breaking zone
Turbulence is important in morphodynamic models as it (i) induces a spatial exchange ofmomentum that affects wave averaged velocities; (ii) it affects the vertical and horizontalmixing of suspended sediment. The present study further shows that breaking inducedturbulence enhances suspended sediment entrainment (Chapter 3) and may also affectbedload transport (Chapter 4) in the surf zone. However, the modelling of TKE in the breakingzone is not trivial as many turbulence closure models seem to systematically overestimate TKEunder both spilling and plunging waves. This has been shown with process based numericalsimulations at high spatial and temporal resolution (i.e. intra wave time scale) and for a rangeof turbulence models, i.e. k (Lin and Liu, 1998; Brown et al., 2016), k (Brown et al., 2016), or,more advanced, large eddy simulation (Christensen, 2006). Further improvement ofturbulence closure models seems essential if near bed TKE is used as input for sedimententrainment or bedload transport. Alternatively, near bed TKE could be predicted throughparameterizations based on wave and bed characteristics. However, near bed TKE is firstlynot fully locally determined as turbulence spreads horizontally and vertically, and secondly itmay not respond instantaneously to forcing at the water surface but is built up over severalwave cycles. For these reasons, a quantitative approach through a more detailed TKE modelseems to be preferred. The further development of such models may benefit from detailedmodel data comparison of the individual terms forming the TKE budget (production,dissipation, transport) under large scale breaking waves.
6.2.3 Suspended sediment transport in breaking zone
Reference concentrations (Co) are predominantly determined by local pick up from the bedand are hardly affected by horizontally advected sediment (Chapter 3). In contrast to nonbreaking waves, C0 seems to be determined by near bed TKE instead of horizontal near bedvelocities. This means that traditional reference concentration/pick up formulae (e.g. Nielsen,1992; Van Rijn, 2007a) may not be appropriate for breaking wave conditions.
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A reference concentration formulation based on near bed TKE was proposed by Steetzel (1991)in the form of C0 = Kc kb3/2, in which Kc is a semi empirical function that depends on sedimentdiameter and which yields values of O(500 kg s3/m6) for medium sand; and kb is the turbulentkinetic energy at the bed. The present experiment supports a direct relation between C0 and kb,although C0 seems to correlate better with kb2 than with kb3/2 (Chapter 3). Steetzel’s (1991) C0formulation is straightforward to implement, but it has not been thoroughly validated becausehardly any datasets contain simultaneous measurements of kb and C0. Other studies havesuggested a direct relationship between C0 and (breaking) wave characteristics (Mocke andSmith, 1992) or between sediment pick up and wave energy dissipation by wave breaking(Kobayashi and Johnson, 2001). Such models assume that wave breaking leads to a local andinstantaneous increase in C0. This is not supported by the present measurements sincebreaking generated turbulence, responsible for the enhanced pick up, spreads horizontallyand vertically and does not arrive instantaneously at the bed at all locations (Chapter 2).
As an alternative to 3D morphodynamic models, depth integrated 1D/2DH models have beendeveloped for research (e.g. Reniers et al., 2004) or engineering purposes (e.g. XBeach: Deltares,2015b). The aforementioned models use an equilibrium concentration approach to calculatethe depth integrated suspended sediment load and transport rates. Effects of breakinginduced turbulent ‘stirring’ to depth integrated suspended load are accounted for by raisingthe rms horizontal velocities through urms,n2 = urms2 + Ks kb. The empirical factor Ks is set equal tounity (Reniers et al., 2004) or to 1.45 (Deltares, 2015, Van Thiel de Vries, 2009) and kb iscomputed through an empirical model based on turbulence at the water surface and assuminga vertical decrease that depends on breaker index (Roelvink and Stive, 1989). The newlycalculated velocity, urms,n is then used to calculate equilibrium concentrations. Using measureddata from the present study, it becomes readily apparent that the addition of kb (=O(0.05 m2/s2))to urms2 (=O(0.5 m2/s2)) does not yield a substantial increase in urms,n2 . This suggests that the effectof wave breaking on suspended sediment load, with a Ks of O(1), can only be substantial if kbis significantly overestimated by the model.
Suspended sediment transport at outer flow elevations is predominantly current related(Chapter 3) and can therefore be properly modeled at wave averaged time scale. However,the wave related transport inside the WBL should be accounted for using a separateformulation as part of suspended (e.g. Van Rijn, 2007b) or of near bed transport (e.g. van derA et al., 2013). Note that Van Rijn (2007b) assumes that wave breaking induces a verticalextension of the wave related transport to the outer flow, and therefore the transport isenhanced with an empirical breaking wave parameter. This vertical extension is supported byprevious measurements that found significant wave related transport at outer flow elevationsunder breaking waves (Houwman and Ruessink, 1996; Grasmeijer, 2002; van Thiel de Vries etal., 2008; Yoon, 2011). However, these observations lack detailed measurements of timevarying (turbulent) velocities near the bed and consequently, it is unclear whether the waverelated suspension is due to the arrival of breaking generated turbulence or due to the verticaladvection by strong upward directed periodic velocities at the wave front of a stronglyasymmetric wave. The present study provides such high resolution measurements but it findslittle support for a vertical extension of wave related transport to the outer flow. Instead, thewave related transport is confined to the WBL (except at one location along the shoreward barslope), similar to previous observations under non breaking waves. This negligible outer flow
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wave related transport may be attributed to the short wave period and the limited temporalvariation in TKE (see Chapter 3). The significance of wave related transport in the breakingregion, and the understanding of the underlying physical processes, requires furtherassessment for a wider range of wave conditions in order to develop a wave related suspendedtransport formulation with a better scientific basis and predictive capability.
6.2.4 Bedload transport in breaking zone
Two topics that can be addressed with the present data are (i) the possible enhancing effectsof breaking generated turbulence on bedload transport; (ii) to what extent bedload transportis still locally determined for the strongly non uniform flow around the breaker bar.
Along the offshore slope up to the breaker bar crest the cross shore variation in bedloadtransport rates is predominantly explained by variations in (dimensional) velocity skewnessand asymmetry (Chapter 4). This is consistent with non breaking waves and the results dotherefore not indicate that an adaptation of existing bedload transport formulations is requiredfor this region. On the other hand, one should be aware that the common application of abedload transport formulation based purely on local forcing is not fully consistent with theunderlying physics. In situations where hydrodynamic conditions vary strongly within thecross shore length of the orbital excursion (e.g. for the present breaking wave setting), bedloaddynamics can be affected by the influx of sediment or of turbulence from adjacent locations.This is illustrated by the sheet flow layer thickness at the bar crest, which is during the troughphase higher than expected based on oscillatory sheet flow observations under non breakingwaves because of a positive cross shore sediment influx. Due to water particle and particleparticle interactions, such non zero sediment influx may affect local bedload transport rates.For such situations the application of bedload transport formulations based only on localforcing may not be fully appropriate, although it is arguably the most straightforward andpragmatic approach for engineering type morphodynamic models.
At the locations between bar crest up to bar trough, i.e. along the steep shoreward facing barslope, bedload transport rates correlate significantly with bed slope and with near bed TKE.Note that due to significant covariation between both parameters, it could not be assessedwhether this correlation is physically induced by either one of the two parameters, or whetherit is the combined effect of both parameters that affects bedload transport rates. Modelformulations have been proposed that account separately for effects by bed slope (Van Rijn,1993) and by near bed TKE (Butt et al., 2004; Reniers et al., 2013) on bedload transport, butalternative formulations based on a combined bed slope/TKE effect have also been proposed(Fernández Mora et al., 2015). Additional experiments that systematically examine theindividual effects by both parameters in the breaking region seem necessary to properlyinclude bed slope and turbulence effects in bedload transport models.
6.2.5 Sediment transport in the swash zone
Many studies (see Chárdon Maldonado et al., 2015, for an overview) have tried to makeexisting bedload transport formulations applicable to swash zone conditions, for instancethrough adapting wave friction factors. Such (adapted) sediment transport formulations havea limited to moderate predictive capability in the swash zone, although this is partly due to
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the large uncertainties in the data used for validation (Chárdon Maldonado et al., 2015).Results inChapter 5 raise three issues regarding the engineering type modeling of net (swashevent averaged) transport in the swash zone:
1. The sheet flow layer does not only respond to hydrodynamic forcing by phaseaveraged velocities, but also to turbulence produced by wave swash interactions. Suchinteractions will likely affect transport rates and should therefore be taken into accountin bedload transport models.
2. Apparently small deviations in offshore hydrodynamic conditions may inducesignificant differences in terms of wave swash interactions. This in return leads toconsiderable variability in bed level changes between swash events at an intra swashand at an event averaged time scale. This high sensitivity of transport rates tohydrodynamic forcing makes it extremely challenging to develop properparameterizations of wave swash interactions effects on bedload transport.
3. The results reveal a complex intra swash cross shore exchange of sediment betweenthe lower and upper swash zone, which affects the sheet flow layer thickness and,consequently, transport rates. Such a time varying horizontal exchange differsessentially from transport in uniform oscillatory sheet flows, and can only be modeledusing detailed intra wave sediment advection/diffusion solvers. At present, such anapproach cannot be easily implemented in morphodynamic models that operate at awave averaged time scale.
Due to these difficulties, and due to additional complex swash zone processes that wereidentified by others (see e.g. Chapter 1), morphodynamic models may achieve better resultsthrough morphological schemes that directly predict bed level changes without resolvingsediment transport rates throughout the swash zone. Such schematizations have already beenproposed (e.g. Walstra and Steetzel, 2003; Van Rijn, 2009) and they typically estimateerosion/accretion in the swash zone by combining the calculated transport rates at theshoreline with an empirical prediction of the wave run up length. However, these schemes donot always yield satisfactory results because they omit much of the relevant physics (Van Rijnet al., 2011). Section 7.2 lists a number of additional swash zone processes that could beincluded to improve such swash zone morphodynamic schemes.
Further development of such model schemes would benefit from high resolutionmeasurements of spatiotemporally varying morphology of the complete swash zone for awide range of wave conditions. Measuring bed level changes in the swash zone has beenchallenging, but novel instrumentation that measures the swash morphology at high spatialand temporal resolution, for instance through stereoscopic imaging (Astruc et al., 2012;Vousdoukas et al., 2014), is becoming increasingly available.
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7 Conclusions and recommendations
7.1 Conclusions
The research questions posed in Chapter 1 were answered through large scale wave flumeexperiments focusing on cross shore sediment transport processes in the surf zone along anevolving breaker bar and in the swash zone. The novelty in these experiments is found in thelarge scale, the application of novel high resolution measurement techniques, and the highspatial temporal coverage of measurements.
A proto type acoustic concentration and velocity profiler (ACVP) was applied to measure, forthe first time under a large scale breaking wave, the hydrodynamics of the wave bottomboundary layer and the spatiotemporal behavior of near bed turbulence. The ACVP alsomeasured near bed sediment fluxes, which offer insights in the complex spatiotemporaladvection of suspended sediment in the surf zone at both an intra wave and a wave averagedtime scale. The measurements further quantify the contributions of bedload and suspendedsediment transport to the onshore migration and growth of the breaker bar. A novelconductivity based measurement system (CCM+) was applied to examine sheet flow dynamicsand bed level changes in the surf and swash zones.
RQ1 (Chapter 2): How does wave breaking affect near bed (wave bottom boundary layer) flowand turbulence?
Near bed hydrodynamics, including turbulent velocities, were measured with the ACVP at 12cross shore locations around an evolving medium sand breaker bar under a regular largescale plunging breaking wave.
Phase averaged wave bottom boundary layer (WBL) velocities show similar behavior to nonbreaking and oscillatory WBL studies, including distinct velocity overshooting. Timeaveraged velocities in the WBL are largely dominated by the strong undertow and showconsistent behavior with previous observations for wave current interactions. Effects of wave(shape) streaming mechanisms are only evident in the shoaling region where the undertow isrelatively weak. Near the plunge point and along the shoreward slope of the bar, thedimensionless WBL thickness is about 3 times higher than predictions based on uniformoscillatory flows. This can be attributed to the combined effects of breaking induced turbulentkinetic energy (TKE) and flow divergence induced by the bed geometry.
Outer flow TKE matches with previous breaking wave studies, showing highest values in thebreaking region at the breaker bar crest, followed by a decrease in the bar trough. In closevicinity of the plunge point (+/ 0.5 m), TKE is almost depth uniform over the complete watercolumn (including the WBL), indicating large turbulence production at the water surface anda strong penetration into the water column down to the bed. Near the plunge point, TKE entersthe boundary layer during two instances of the wave cycle: a first occurrence rapidly (about0.5 s) after wave plunging, when breaking induced TKE rapidly saturates the complete watercolumn including the WBL; a second occurrence during the wave trough phase, when
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undertow and periodic velocities transport TKE towards the breaker bar. This invasion resultsin an increase in maximum TKE inside the WBL with a factor of almost three and in an increasein near bed Reynolds stress magnitudes with about a factor two between shoaling andbreaking region, despite decreasing near bed periodic velocity magnitudes.
Breaking generated turbulence travels horizontally offshore (during trough phase) and backonshore (during crest phase) between breaking and shoaling zone. Due to advection byperiodic and offshore directed time averaged velocities, the area affected by breakinggenerated turbulence extends from the breaking region to shoaling locations about 3 m (i.e. 6times the semi excursion amplitude) offshore from the plunge point. Advection of TKE fromplunge point in onshore direction is restricted by the combination of a decreased orbitalvelocity amplitude and strong offshore directed undertow velocities.
RQ2 (Chapter 3):How are suspended sediment transport processes affected by wave breaking?
Suspended sediment concentrations and fluxes were measured with the ACVP at the same 12cross shore locations covering the shoaling to inner surf zone, with particular high resolutionin the lowest 0.10 m that includes the WBL.
Sediment pick up rates increase with up to an order of magnitude from shoaling to breakingregion. Wave averaged reference concentrations in the breaking region correlate better withnear bed TKE than with bed parallel periodic velocities, suggesting that breaking generatedturbulence is an important driver for sediment pick up. At an intra wave time scale,suspended sediment concentrations are phase coherent with near bed TKE. Suspendedsediment is particularly well mixed above the bar crest, where outer flow concentrations arenearly depth uniform. This vertical mixing is attributed to the combination of energeticbreaking generated vortices, the strongly asymmetric wave shape (strong upward waverelated advection), and upward directed wave averaged velocities resulting from a timeaveraged fluid circulation cell.
Net (i.e. wave averaged) suspended sediment fluxes reveal a complex pattern with verticallyalternating onshore and offshore directed constituents. Net outer flow fluxes are generallycurrent related and are directed offshore due to the undertow. Above the breaker bar, netonshore fluxes between wave trough and wave crest level contribute significantly to the depthintegrated suspended transport. Net fluxes inside the WBL are directed onshore at shoalinglocations and at breaking locations up to the bar crest due to significant wave related fluxcontributions. The net wave related suspended transport is generally confined to the WBL,except at the breaking location with highest near bed TKE where net wave related fluxesextend vertically to outer flow elevations.
Sediment flux gradients were quantified to study the advection and the pick up/deposition ofsuspended sediment. At a wave averaged time scale, sediment grains are entrained from thebed in the bar trough region, are advected offshore by the undertow, and are deposited in theregion covering the shoaling zone, bar crest, and the upper part of the steep onshore bar slope.Wave averaged near bed concentrations are largely (>90%) determined by local pick up;contributions of cross shore advected sediment are minor.
The flux gradients at intra wave time scale reveal that the entrainment of sediment in the bartrough occurs primarily during the wave trough phase, when both near bed velocity
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magnitude and near bed (breaking generated) TKE are highest. The entrained particles arealmost instantly advected offshore during the wave trough phase. Net deposition near the barcrest occurs during the wave crest phase when velocity magnitudes reduce. The suspendedparticles further follow an onshore offshore excursion between shoaling and breaking regionat an intra wave time scale. This excursion is consistent with spatiotemporal patterns in TKE,which suggests that sediment particles are trapped in breaking generated vortices that areadvected back and forth following the orbital motion.
RQ 3 (Chapter 4):How are bedload processes affected by wave breaking and how do suspendedand bedload transport contribute to breaker bar morphodynamics?
During the same experiment with regular plunging waves, sheet flow layer dynamics weremeasured just offshore from the breaker bar crest using the CCM+. The sheet flow thickness atthe offshore bar slope scales similarly to hydrodynamic forcing as previous observationsunder non breaking waves. At the bar crest, horizontal sediment advection along the bedaffects sheet flow concentrations and thicknesses during the wave trough phase due to apositive influx of sediment.
The net total transport rate along the breaker bar is decomposed into measured suspendedload and bedload contributions. Bedload and suspended load transport are of similarmagnitude but of opposite direction. Onshore directed bedload transport dominates at theshoaling zone, decreases at the bar crest, and increases again at the shoreward facing bar slope.The latter is explained by bed slope effects (i.e. gravity driven transport) and occurs inpresence of high near bed TKE, that possibly enhances the mobilization of sand grains. Theoffshore directed suspended transport rate increases in the breaking region, leading to adomination of suspended transport over bedload transport in the breaking and inner surfzone. Consequently, near the plunge point the net total transport rate reverses from onshoredirected (shoaling zone) to offshore directed (breaking and inner surf zone).
During the experiment, the breaker bar crest increases in height while the bar trough deepens.Both bedload and suspended sediment transport contribute to breaker bar morphodynamics,but the effect of each component is notably different. Bedload transport leads to erosion of theoffshore bar slope and accretion at the bar crest, and additionally leads to erosion of the steepshoreward bar slope and deposition at the bar trough. Suspended transport induces erosionof the bar trough and net deposition at the breaker bar crest.
Suspended sediment samples reveal evident vertical grain sorting at the shoaling and innersurf zone, which indicates that sediment pick up and vertical mixing is size selective (i.e. thefraction of fine sediment increases with elevation). This contrasts the breaking region, wheresediment pick up and vertical mixing is size indifferent due to the strong upward forcing bylarge scale energetic vortices and upward time averaged velocities. Bed samples reveal crossshore sorting of sand particles by size selective bedload and suspended load transport. Thissorting leads to a gradual increase in sediment diameter from shoaling to inner surf zone andreveals additional local sorting around the breaker bar due to bed slope effects (i.e. downwardcoarsening along the steep shoreward bar slope).
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RQ 4 (Chapter 5): How do swash processes such as wave swash interactions and cross shoreintra swash advection of sediment affect bed level changes and sheet flow layer dynamics?
During another experiment, the CCM+ was deployed for the first time to measure bed levelchanges and sheet flow dynamics at the lower swash zone during a complete swash cycle.
Intra swash bed level changes follow a consistent pattern of rapid bed erosion during the earlyuprush and gradual accretion during the middle backwash phase. Subtle differences inhydrodynamics between the various wave groups lead to substantial differences in both themagnitude of the intra group bed level fluctuations (6 13 mm) and in the net bed level change(2 3 mm erosion or accretion) induced by each wave group. This causes the bed to respond notonly at the group frequency of the bichromatic waves, but also at the repeat frequency of thewave group sequence.
Sheet flow transport was observed at the early uprush and during the middle and latebackwash phase. At the early uprush, the growth of the sheet flow layer and the drop in bedlevel occur almost simultaneously. The sheet flow layer exhibits some features similar tooscillatory sheet flow, such as sediment entrainment from the pick up layer. This pick up isobserved not only when horizontal shear velocities are high, but also in occurrence of waveswash interactions during the backwash. Direct cross shore sediment flux measurements inthe sheet flow layer show similarities with oscillatory sheet flow conditions, with highest fluxrates found in the pick up layer.
Notable differences from observations of oscillatory sheet flow are (i) a time varying elevationof the concentration pivot point within a wave group cycle; (ii) an absence of mirroringconcentration behavior in pick up layer and upper sheet flow layer. These differences relateto the highly non uniform flow: horizontal sediment advection affects the upper sheet flowlayer concentrations, i.e. the properties of the sheet flow layer are not fully locally determined.
7.2 Recommendations
This section presents recommendations for further research steps towards improvingmorphodynamic modeling of the surf and swash zones on the basis of the new experimentalresults in this thesis. Distinction is made between three research topics (surf zone suspendedload, surf zone bedload, and swash zone sediment transport). For each topic, suggestions aremade for improving sand transport model formulations, i.e. through model data comparisonsand through additional numerical/experimental research that can help to improve processinsights.
Suspended transport in the surf zone
An important step is the inclusion of breaking generated turbulence effects on suspendedsediment pick up/reference concentrations. Formulations are available (e.g. Mocke and Smith,1992; Steetzel, 1993; Kobayashi and Johnson, 2001; Reniers et al., 2004) but require morethorough validation against suspension measurements for a wide range of large scalebreaking wave conditions (including the present dataset). The further development of suchformulations would benefit from a better understanding of the physical mechanism ofsediment pick up by breaking generated vortices. Measurements of pore pressure in the bed
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under a large scale breaking wave may contribute to explain the pick up behavior (c.f. Sumeret al., 2013).
Pick up formulations based on near bed turbulence can only be implemented if near bed TKEis properly predicted. Given the poor performance of present turbulence closure models inpredicting near bed TKE (Brown et al., 2016), simplified approaches (e.g. Roelvink and Stive,1989) or empirical predictions for near bed TKE could be considered. However, suchformulations would also require a thorough validation against measurements for a wide rangeof breaking wave and sediment bed conditions. The performance of turbulence closure modelsmay benefit from surf zone studies that present not only the spatiotemporal variation in TKEbut also quantify various terms of the TKE budget (c.f. Van der A et al., Submitted).
The modelling of wave related suspended transport inside and/or above the WBL requiresadditional experimental research. In the present study, the wave related transport is generallyconfined to the WBL (as is the case for non breaking waves) although it can locally extend toouter flow elevations. This apparent inconsistency with previous surf zone observations atouter flow elevations may be due to the short wave period compared to typical turbulencedecay times for this particular wave condition (Section 6.2.3) . Additional high resolutionmeasurements of near bed sediment fluxes for a wider range of wave conditions – particularlylonger period or irregular waves with an expectedly stronger intra wave variation in near bedTKE – may benefit the further development of wave related suspended transportformulations.
The data in this thesis allow validation and improvement of formulations for size selectivesuspended sediment pick up and vertical mixing (e.g. Van Rijn, 2007c).
Bedload transport in the surf zone
Bedload transport formulations in the surf zone may need to account for effects of intermittenthigh bed shear stresses that are expected based on the invasion of TKE into the WBL. Sucheffects could in combination with local sloping bed lead to an additional net transportcontribution. The present measurements could be used to validate existing bedload transportmodels used in combination with parameterizations for bed slope effects and TKE.
The insights in wave breaking effects on bedload transport remain still somewhat restrictedafter this study. Sheet flow layer observations at the breaker bar crest did not reveal asignificant effect of breaking generated turbulence. However, such effects may still occuralong the shoreward facing bar slope where the invasion of breaking generated turbulenceinto the WBL is much stronger. Additional sheet flow measurements at this particular locationwould improve process insights, but such measurements are challenging due to the evolvingand steep bed. Therefore, one may instead consider experiments in an oscillatory flow tunnelusing grid turbulence to study the effects of external TKE on oscillatory bedload transportprocesses and transport rates. Such an experiment could be more easily done for a wide rangeof wave and sediment bed conditions and would also isolate TKE effects from bed slopeeffects. Grid turbulence has been used before to study effects of external turbulence on WBLdynamics for a rigid bed (Fredsoe et al., 2003) and on bedload transport in steady flows (Sumeret al., 2003). Effects of time varying turbulence could be examined by running asymmetricflows that would result in different grid induced TKE for each half cycle.
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Simulations of sheet flow layer dynamics with detailed process based models (e.g.Kranenburg et al., 2014; Finn et al., 2016) can offer another approach in understanding theeffects of external (breaking generated) turbulence on bedload transport rates. Such localprocess based models, or process based morphodynamic models that operate at an intra wavetime scale, may also be used to assess the effects of cross shore sediment influx on localbedload transport rates, i.e. to assess whether bedload transport in such a non uniformbreaking wave setting is still locally controlled.
Bedload transport models also rely on an appropriate hydrodynamic input of local near bedvelocities, including the velocity and acceleration skewness. Although existing skewnessparameterizations may capture the overall trend of wave deformation from shoaling to innersurf zone (e.g. Ruessink et al., 2012), they do not include the local wave deformation aroundthe breaker bar where the wave breaks. Given the significance of this deformation in affectingbreaker bar morphodynamics (through cross shore varying bedload transport rates), thenumerical reproduction of bar morphodynamics would benefit from further improvement ofvelocity skewness and asymmetry parameterizations for the breaking region. Existingparameterizations may be improved on the basis of numerical data created with process basednumerical models, as existing process based RANS models seem to properly predict velocityskewness and asymmetry patterns (e.g. Torres Freyermuth et al., 2010; Jacobsen et al., 2014).
Sediment transport in the swash zone
For the swash zone, it is recommended to further develop modeling schemes for bed evolutionin the swash zone, based on existing formulations (e.g. Walstra and Steetzel, 2003; Van Rijn,2009). Results in the present study particularly illustrate the significance of wave swashinteractions and of intra swash cross shore sediment advection. The degree of wave swashinteractions can be parameterized based on the relative swash event duration (Alsina et al.,2009), which in turn can be estimated based on bed slope and wave breaking parameters(Pujara et al., 2015b). The cross shore variation in transport rates may be parameterized basedon the combination of breaker type and cross shore velocities at the shoreline, which wasfound to control the bed shear along the swash zone (Pujara et al., 2015a).
Such numerical morphodynamic schemes require proper datasets that ideally include (i) highresolution (spatially and temporally) measurements of swash zone bed evolution at event byevent time scale, which can be used to quantify transport rates along the swash and the totalsediment load entering/leaving the swash zone (by solving the Exner equation); (ii)measurements of offshore hydrodynamic forcing parameters. Although such datasets arecurrently scarce – if not non existent – such measurements could be acquired through noveltechniques for measuring the complete swash zone morphology (e.g. stereoscopic imaging).
Swash zone sediment transport processes have predominantly been examined in the fieldwhere typically only a few cross shore locations were covered. Most laboratory studiesfocused on hydrodynamic processes of (bore driven) swash on rigid beds. Experiments thatsystematically cover the complete swash zone with high spatial and temporal resolution arepresently lacking, but may greatly improve insights on effects of intra swash sedimentadvection on spatiotemporally varying bed levels.
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van der A, D. A., T. O Donoghue and J. S. Ribberink (2010).Measurements of sheet flow transportin acceleration skewed oscillatory flow and comparison with practical formulations. CoastalEngineering 57(3): 331 342. doi: 10.1016/j.coastaleng.2009.11.006.
van der A, D. A., T. O’Donoghue, A. G. Davies and J. S. Ribberink (2011). Experimental study ofthe turbulent boundary layer in acceleration skewed oscillatory flow. Journal of FluidMechanics 684: 251 283. doi: 10.1017/jfm.2011.300.
van der A, D. A., J. S. Ribberink, J. J. van der Werf, T. O Donoghue, R. H. Buijsrogge and W.M. Kranenburg (2013). Practical sand transport formula for non breaking waves andcurrents. Coastal Engineering 76: 26 42. doi: 10.1016/j.coastaleng.2013.01.007.
van der A, D. A., J. Van der Zanden, T. O Donoghue, I. Cáceres, S. J. McLelland and J. S.Ribberink (Submitted). Hydrodynamics and turbulence under a large scale plunging waveover a fixed bar. Journal of Geophysical Research: Oceans. doi.
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About the author
200
About the author
Joep van der Zanden was born in Roermond, the Netherlands,on the 11th October 1987 and grew up in Someren in theprovince of Noord Brabant. After finishing his pre universitysecondary education at Het Varendonck College in Asten in2005, he enrolled in the BSc study ‘Soil, Water andAtmosphere’ at Wageningen University which he completedin 2008 with a graduation project focusing onmorphodynamic processes in a river flume with a cohesivebed.
After a full time board year as secretary of students sports foundation Thymos, Joep startedhis MSc ‘Hydrology and Water Management’ at Wageningen University. He obtained his MScdegree in 2012 after a six month graduation project on numerical modeling of groundwater–vegetation interactions, conducted at the University of Sydney, and a five month internship atHydrologic (Netherlands). During his studies, Joep participated in extracurricular activities byhis study association and several sports organizations in Wageningen.
Joep moved to Enschede in 2012 to start his PhD research at the Water Engineering andManagement department of the University of Twente. During his PhD research he spent oversix months in Barcelona to participate in four experimental campaigns in the CIEM waveflume. He further tutored seminars during courses at BSc and MSc level and (co )supervisedfour BSc and three MSc graduation projects. In 2016, he froze his PhD research for a six monthresearch assistant position at the University of Aberdeen, UK. He presented his researchresults at international conferences in Lisbon, San Diego, Schoorl and Edinburgh.
In his free time Joep enjoys outdoor sports activities (running, cycling). He further enjoyslistening music and guitar playing. His holidays are best spent by exploring new groundsthrough trekking in nature.
About the author
201
Publications
Peer reviewed journal papers
van der Zanden, J., J. M. Alsina, I. Cáceres, R. H. Buijsrogge and J. S. Ribberink (2015). Bed levelmotions and sheet flow processes in the swash zone: Observations with a new conductivity basedconcentration measuring technique (CCM+). Coastal Engineering 105: 47 65. doi:10.1016/j.coastaleng.2015.08.009.
van der Zanden, J., D. A. van der A, D. Hurther, I. Cáceres, T. O Donoghue and J. S. Ribberink(2016). Near bed hydrodynamics and turbulence below a large scale plunging breaking wave over amobile barred bed profile. Journal of Geophysical Research: Oceans 121(8): 6482 6506. doi:10.1002/2016jc011909.
van der Zanden, J., D. A. van der A, D. Hurther, I. Caceres, T. O Donoghue and J. S. Ribberink(submitted). Suspended sediment transport around a large scale laboratory breaker bar. CoastalEngineering
van der A, D. A., J. van der Zanden, T. O Donoghue, I. Cáceres, S. J. McLelland and J. S.Ribberink (submitted). Hydrodynamics and turbulence under a large scale plunging wave over afixed bar. Journal of Geophysical Research: Oceans.
van der Zanden, J., D. A. van der A, D. Hurther, I. Caceres, T. O Donoghue, S. J. M. H. Hulscherand J. S. Ribberink (in preparation). Bedload and suspended load contributions to themorphodynamics of a large scale laboratory breaker bar.
Non reviewed papers
van der Zanden, J., J.S. Ribberink, S.J.M.H. Hulscher and D.A. van der A (2016). Betere modellennodig voor zandtransport onder brekende golven. Land en Water 2016(12)
Ribberink, J.S., T. O Donoghue, D.A. van der A, J. van der Zanden, D. Hurther, I. Cáceres andP.D. Thorne (2014). Measurements of sand transport processes under breaking and irregular waves.IAHR newsletter 2014(3), 86 87.
van der Zanden, J. (2014). Het effect van golfbreking op zandtransport. ConcepTueel, 23(2), 24 27.
Conference papers
van der Werf, J. J., R. Veen, J. S. Ribberink and J. van der Zanden (2015). Testing of the newSANTOSS transport formula in the Delft3D morphological modeling system. Proc. of CoastalSediments. San Diego, USA: 14 pp.
van der Zanden, J., D. A. van der A, J. S. Ribberink, T. O Donoghue, D. Hurther, I. Caceres andP. D. Thorne (2015). Sand transport process measurements under large scale breaking waves. Proc.of Coastal Sediments. San Diego, USA: 14 pp.
About the author
202
Alsina, J., I. Caceres, J. van der Zanden, J. S. Ribberink and T. E. Baldock (2014). Large scaleexperiments on beach evolution induced by bichromatic wave groups with varying group period. Proc.of the 34th ICCE, Seoul, Korea: 10 pp.
Alsina, J. M., J. van der Zanden, J. S. Ribberink, R. H. Buijsrogge, T. E. Baldock, M. Brocchini,E. Peña, F. Sanchez Tembleque and I. Caceres (2014). Sediment transport and beach profileevolution induced by bichromatic waves with different grouping periods. Proc. of the HYDRALABIV Joint User Meeting, Lisbon
Ribberink, J. S., D. A. van der A, J. van der Zanden, T. O Donoghue, D. Hurther, I. Cáceres andP. D. Thorne (2014). SandT Pro: Sediment transport measurements under irregular and breakingwaves. Proc. of the 34th ICCE, Seoul, Korea. P. Lynett. 14 pp.
van der Zanden, J., J. M. Alsina, I. Cáceres, R. H. Buijsrogge and J. S. Ribberink (2013). NewCCM technique for sheet flow measurements and its first application in swash zone experiments. Proc.of Short Course/Conference on Applied Coastal Research, Lisbon, Portugal, 10 pp.
Presentations at national and international conferences:
Oral presentations at SCACR (Lisbon, Portugal, 2013),NCK Days (Schoorl, Netherlands, 2015),Coastal Sediments (San Diego, USA, 2015), Scottish Fluid Mechanics meeting (Edinburgh, UK,2016).
Poster presentations at NCK Days (2013, 2014, 2016).
Teaching experience
BSc Civil Engineering courses at University of Twente:
Fluid Mechanics (seminar tutoring)
MSc Civil Engineering and Management courses at University of Twente:
Mathematical Physics in Water Systems (seminar tutoring)
Data Analysis in Water Engineering and Management (Matlab/ArcGIS seminars)
Marine Dynamics (seminar tutoring)
Academic Research Skills, pre master (supervising practical assignment)
Seminar morphology (supervising practical assignment)
(co )Supervision of three MSc graduation projects and four BSc graduation projects.
Awards
Nominated for Twente Water Centre ‘PhD paper of the year’, 2016.
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